Exact native proof sources
Every file linked below is the complete unchanged original editable source at its listed pinned revision. The corpus retains human Stacks authorship and credited AI Integrated Stacks contributions under the source terms. It is a bounded proof-source package, not a claimed standalone build of the entire Stacks distribution.
The exact hashes, original paths, public pinned identities and scoped dependency edges are in native-manifest.json.
COPYING
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 4b2c8fc390f802cd92f0622dc00a708a588bec54d0145d2ee135d6d7672bfe85; 20404 bytes.
PROVENANCE.md
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 720213712ef43614e42a79feee1bb540a326a6aba81a179533593c33d4123122; 17610 bytes.
README.md
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 eea487dda718bc94faef3d343515eebe465cb39d19b098aa08f36f0d01cb2400; 16925 bytes.
algebra.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 2789bc69c75351b0840206c4bc7ec6db0a7cc7765e1f7ecc1cfa671ea80d64cd; 1808110 bytes.
- algebra-definition-analytically-unramified, line 46582.
- algebra-example-spec-kxy, line 4948.
- algebra-lemma-CM-over-regular-flat, line 33409.
- algebra-lemma-Noetherian-complete-local-Nagata, line 46556.
- algebra-lemma-analytically-unramified-easy, line 46609.
- algebra-lemma-apply-grothendieck, line 47185.
- algebra-lemma-complete-local-Noetherian-domain-finite-over-regular, line 45847.
- algebra-lemma-completion-Noetherian, line 23557.
- algebra-lemma-completion-faithfully-flat, line 23523.
- algebra-lemma-completion-finite-extension, line 23681.
- algebra-lemma-completion-flat, line 23502.
- algebra-lemma-criterion-normal, line 44733.
- algebra-lemma-derivative-zero-pth-power, line 44936.
- algebra-lemma-descend-properties-modules, line 20853.
- algebra-lemma-descent-Rk, line 47573.
- algebra-lemma-descent-Sk, line 47546.
- algebra-lemma-descent-normal, line 47495.
- algebra-lemma-descent-regular, line 47526.
- algebra-lemma-dim-affine-space, line 28385.
- algebra-lemma-dimension-base-fibre-total, line 28116.
- algebra-lemma-exact-sequence-NL, line 36167.
- algebra-lemma-finite-projective, line 19558.
- algebra-lemma-finite-projective-descends, line 19815.
- algebra-lemma-generically-finite, line 31169.
- algebra-lemma-hathat-finitely-generated, line 23191.
- algebra-lemma-integral-under-field, line 7823.
- algebra-lemma-local-nagata-domain-analytically-unramified, line 46766.
- algebra-lemma-nagata-in-reduced-finite-type-finite-integral-closure, line 46439.
- algebra-lemma-regular-domain, line 26261.
- algebra-lemma-regular-graded, line 26237.
- algebra-lemma-regular-mod-x, line 26379.
- algebra-lemma-regular-normal, line 44808.
- algebra-lemma-regular-ring-CM, line 26278.
- algebra-lemma-separable-smooth, line 39495.
- algebra-lemma-support-point, line 15446.
- algebra-proposition-dimension, line 14981.
- algebra-proposition-ubiquity-nagata, line 47030.
- algebra-section-blow-up, line 17619.
- algebra-section-completion-noetherian, line 23440.
- algebra-section-going-up, line 9573.
algebraic.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 08445616a6bb3555d25b8b589daf3faaf68e8ca5aa0bd7ce85e6332740d7dfcb; 97496 bytes.
- algebraic-lemma-characterize-representable-by-space, line 454.
- algebraic-lemma-criterion-map-representable-spaces-fibred-in-groupoids, line 552.
- algebraic-lemma-representable-morphism-to-algebraic, line 1955.
- algebraic-section-morphisms-representable-by-algebraic-spaces, line 497.
- algebraic-section-representable-morphism, line 211.
- algebraic-section-representable-properties, line 838.
bibliography.tex
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 417f904daa77cc42e74d99f4f5647f5cb79c14cc15631a43770a97f432aa1243; 165 bytes.
bootstrap.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 fd2b99bb99e4ab6ea55491ca819e4964097dc504403b5b306c455614d5ff9f27; 96614 bytes.
chow.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 0522bd9a5934c5a65d9fccd651c77c1e012d9937aec49737d0b7fea6190dc001; 688563 bytes.
coherent.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 d219cba93ea84084a35be94b3454e316c54037af0bfbf795a1824543d9440bbc; 357482 bytes.
- coherent-lemma-chow-Noetherian, line 5823.
- coherent-lemma-coherent-support-dimension-0, line 2652.
- coherent-lemma-cohomology-projective-space-over-ring, line 1670.
- coherent-lemma-flat-base-change-cohomology, line 1015.
- coherent-lemma-formal-functions-stalk, line 6634.
- coherent-lemma-higher-direct-images-zero-above-dimension-fibre, line 6743.
- coherent-lemma-kill-by-twisting, line 5327.
- coherent-lemma-power-ideal-kills-sheaf, line 2733.
- coherent-lemma-proper-over-affine-cohomology-finite, line 6127.
- coherent-lemma-recover-tail-graded-module, line 4118.
- coherent-lemma-relative-affine-cohomology, line 234.
- coherent-lemma-vanishing-nr-affines, line 646.
- coherent-lemma-vanshing-gives-ample, line 5416.
- coherent-proposition-proper-pushforward-coherent, line 6008.
- coherent-theorem-formal-functions, line 6561.
cohomology.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 591f19389ef437ddfe05b00214064dda31aa225d44b019a779f9f98f6ec0b4de; 539704 bytes.
- cohomology-lemma-Leray, line 2262.
- cohomology-lemma-h1-extensions, line 351.
- cohomology-lemma-projection-formula, line 14351.
- cohomology-lemma-quasi-separated-cohomology-colimit, line 3575.
- cohomology-proposition-vanishing-Noetherian, line 4051.
constructions.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 cfebd4fe907082611f346447285454e473fc35f68ed3f10494c412547cf80fad; 209942 bytes.
- constructions-lemma-base-change-map-proj, line 2663.
- constructions-lemma-globally-generated-omega-twist-1, line 3622.
- constructions-lemma-proj-quasi-compact, line 1517.
- constructions-lemma-proj-separated, line 1491.
- constructions-lemma-projective-space, line 3231.
- constructions-lemma-surjective-graded-rings-generated-degree-1-map-proj, line 2637.
curves.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 8881792e2c8e0977e778827b852b010af11f054f98866c61beb5dffe70515ebe; 271533 bytes.
- curves-lemma-torsion-picard-becomes-visible, line 3439.
- normalization/gluing torsion and multicross equality in Section53.
decent-spaces.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 761d71fa0c53320fe2ec7f1063c667a5a0172a4d789ab4a3ba8e4ca1ecb4c69f; 223472 bytes.
- decent-spaces-lemma-bounded-fibres, line 735.
- decent-spaces-lemma-quasi-compact-reasonable-stratification, line 1436.
derham.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 0aa0f22d9765ccbb167d3c63d47143acd35b241972b6b71fc772d8f0b327cdf3; 237942 bytes.
- derham-example-Garel, line 4132.
- derham-proposition-Garel, line 4012.
- derham-section-trace, line 3815.
descent.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 ef34f287456e31eb5a359279d24dc089b70191223de396a0f1f50c52fc83577c; 395223 bytes.
- descent-lemma-descending-fppf-property-immersion, line 7410.
- descent-lemma-reduced-local-smooth, line 6046.
divisors.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 4c022ef77f817b5a8f8f1a2368cda9c711a65e68209b58aaf14e2703418ded4f; 379689 bytes.
- divisors-definition-admissible-blowup, line 9219.
- divisors-definition-blow-up, line 8414.
- divisors-definition-divisor-invertible-sheaf, line 6868.
- divisors-lemma-Pic-projective-space-UFD, line 7385.
- divisors-lemma-S1-no-embedded, line 411.
- divisors-lemma-blow-up-and-irreducible-components, line 8671.
- divisors-lemma-blow-up-integral-scheme, line 8659.
- divisors-lemma-blow-up-pullback-effective-Cartier, line 8697.
- divisors-lemma-blowing-up-affine, line 8452.
- divisors-lemma-blowing-up-gives-effective-Cartier-divisor, line 8513.
- divisors-lemma-blowing-up-projective, line 8753.
- divisors-lemma-blowup-fitting-ideal, line 9470.
- divisors-lemma-characterize-affine-blowup, line 8600.
- divisors-lemma-characterize-effective-Cartier-divisor, line 2403.
- divisors-lemma-codim-1-part, line 3076.
- divisors-lemma-conormal-effective-Cartier-divisor, line 2702.
- divisors-lemma-conormal-sheaf-section-projective-bundle, line 8320.
- divisors-lemma-describe-reflexive-hull, line 2304.
- divisors-lemma-effective-Cartier-divisor-is-a-sum, line 3194.
- divisors-lemma-extend-invertible-module, line 7257.
- divisors-lemma-extend-rational-map-after-modification, line 9582.
- divisors-lemma-flat-base-change-blowing-up, line 8481.
- divisors-lemma-integral-effective-Cartier-divisor-dvr, line 3006.
- divisors-lemma-invertible-sheaf-sum-effective-Cartier-divisors, line 2746.
- divisors-lemma-normal-c1-injective, line 6934.
- divisors-lemma-normal-effective-Cartier-divisor-S1, line 3044.
- divisors-lemma-open-subscheme-UFD, line 7317.
- divisors-lemma-pullback-effective-Cartier-defined, line 2595.
- divisors-lemma-reflexive-over-regular-dim-2, line 2337.
- divisors-lemma-restriction-injective-open-contains-weakly-ass, line 652.
- divisors-lemma-section-smooth-regular-immersion, line 5614.
- divisors-lemma-ses-add-divisor, line 2714.
- divisors-lemma-sum-effective-Cartier-divisors, line 2505.
- divisors-lemma-universal-property-blowing-up, line 8564.
- divisors-lemma-wedge-product-ses, line 3277.
duality.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 2a0b9b65c79ec3fb149937b8b65cdb0a0021360637b46bdce9334ae1989f8287; 360284 bytes.
- duality-example-iso-on-RSheafHom-noetherian, line 648.
- duality-example-proper-over-local, line 5874.
- duality-lemma-duality-bootstrap, line 5392.
- duality-lemma-dualizing-module, line 5905.
- duality-lemma-dualizing-module-CM-scheme, line 6018.
- duality-lemma-gorenstein-base-change, line 6284.
- duality-lemma-gorenstein-morphism, line 6339.
- duality-lemma-regular-gorenstein, line 6193.
- duality-lemma-sheaf-with-exact-support-effective-Cartier, line 3228.
- duality-lemma-shriek-dualizing, line 4512.
- duality-lemma-twisted-inverse-image-closed, line 2250.
- duality-section-duality, line 4961.
- duality-section-dualizing-module, line 5835.
- duality-section-glue, line 5054.
- duality-section-trace, line 1616.
dualizing.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 b1262987c3041fd1b15fbae46a0cc66dc9ba2c28917ed32330e4904981b131c2; 210693 bytes.
- dualizing-lemma-gorenstein-divide-by-nonzerodivisor, line 3908.
- dualizing-lemma-regular-gorenstein, line 3779.
- dualizing-lemma-special-case-local-duality, line 3526.
- dualizing-lemma-ubiquity-dualizing, line 4142.
- dualizing-proposition-matlis, line 968.
- dualizing-section-dualizing-local, line 2922.
examples-stacks.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 54dbc9d017b82b7c93a6ccd72a0295e5a2c1a3e535187083e4100101cd577976; 65671 bytes.
examples.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 67a1c8c75378391e6282040f4cdbd873a5f9b00e3261b49588116a6a7305c5f5; 277677 bytes.
fdl.tex
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 41f30f5c60d0d61012e3ba7d80ad27be062b7132d84ade3102e460e619e9a9f6; 21760 bytes.
fields.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 0b263dfe4e10eaae84a317703ca5de47ced45aad67518726b06caf340dd4d0fa; 144567 bytes.
flat.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 b4d84512290a62109009ed1a6e9ce4b58d09a566589cae90fecf88efb630a804; 563759 bytes.
- flat-lemma-dominate-modification-by-blowup, line 9222.
- flat-lemma-finite-after-blowing-up, line 9173.
groupoids.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 906061343b5f46807a99fb3843ba9ef60b6fbe3d9daddc1aa964aeafaa9a59b7; 205809 bytes.
- groupoids-definition-abelian-variety, line 1764.
- groupoids-proposition-review-abelian-varieties, line 2071.
introduction.tex
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 43abd6493bf48325878d6573966e97025770d4b4e12db1dda31da7fd181d4acf; 6560 bytes.
limits.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 dccddc3622ebad21dd6219ea50b157fcf20c574e82b9e920b7f4d1ed127e0aa4; 222594 bytes.
models.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 5cfa014ca4381c99333043af35ed443f10e083fa601f854f78770b71c9a5f98b; 205089 bytes.
- models-theorem-semistable-reduction, line 6640.
- models-lemma-bound-wm, line 3955.
- models-lemma-equality-genus-reduction-bigger-than, line 5324.
- models-lemma-sequence-torsion, line 5746.
- models-lemma-torsion-embeds, line 5778.
moduli-curves.tex
Complete local source · exact pinned version
Role: native source comparator. SHA256 d4dba83e25d3aea239197824bca0706b650917000540ef4d324a87feaeaf41fe; 128255 bytes.
- Native comparison only: current owned AG-AS supplies stabilization, uniqueness and tricanonical frame construction.
more-algebra.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 0490028f82effcf08c0d790d0c8145eeb8d55db66bfb8cf7ba29ccd27fc3fabe; 1518081 bytes.
- more-algebra-definition-extension-discrete-valuation-rings, line 33535.
- more-algebra-lemma-application-formal-glueing, line 25505.
- more-algebra-lemma-completion-dimension, line 11234.
- more-algebra-lemma-completion-dvr, line 11297.
- more-algebra-lemma-completion-regular, line 11278.
- more-algebra-lemma-dedekind-torsion-free-flat, line 4958.
- more-algebra-lemma-divides-radical, line 38862.
- more-algebra-lemma-finite-type-over-excellent, line 13983.
- more-algebra-lemma-isomorphic-completions, line 29747.
- more-algebra-lemma-normal-goes-up, line 11163.
- more-algebra-lemma-power-series-ring-subfields, line 12131.
- more-algebra-lemma-regular-local-UFD, line 37424.
- more-algebra-proposition-ubiquity-J-2, line 12555.
- more-algebra-proposition-ubiquity-excellent, line 13996.
- more-algebra-remark-finite-separable-extension, line 33629.
- more-algebra-remark-formal-glueing-algebras, line 25659.
more-morphisms.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 6f36e5ff2c2b5c66fc2aa762421f0024c08c409ab86d1d814f70a065f416475a; 976082 bytes.
morphisms.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 51cfcb7402d0e84aad95bdb6dd8840552f6f635fc20709521fd4ab895df05242; 593209 bytes.
- morphisms-definition-alteration, line 13700.
- morphisms-definition-birational, line 13129.
- morphisms-definition-modification, line 13679.
- morphisms-definition-normalization, line 14526.
- morphisms-definition-quasi-projective, line 9735.
- morphisms-definition-scheme-theoretic-image, line 824.
- morphisms-example-scheme-theoretic-image, line 887.
- morphisms-lemma-H-quasi-projective-open-H-projective, line 10724.
- morphisms-lemma-algebraic-residue-field-extension-closed-point-fibre, line 3574.
- morphisms-lemma-base-change-differentials, line 6660.
- morphisms-lemma-base-change-proper, line 9939.
- morphisms-lemma-characterize-proper, line 10203.
- morphisms-lemma-characterize-relatively-ample, line 8689.
- morphisms-lemma-composition-projective, line 10827.
- morphisms-lemma-composition-proper, line 9919.
- morphisms-lemma-composition-quasi-projective, line 9776.
- morphisms-lemma-conormal-functorial, line 6221.
- morphisms-lemma-conormal-functorial-flat, line 6287.
- morphisms-lemma-differentials-relative-immersion, line 6744.
- morphisms-lemma-dimension-fibre-after-base-change, line 5434.
- morphisms-lemma-dimension-formula, line 13729.
- morphisms-lemma-extend-across, line 10446.
- morphisms-lemma-finite-birational-over-normal, line 14777.
- morphisms-lemma-finite-proper, line 11183.
- morphisms-lemma-finite-type-nagata, line 3266.
- morphisms-lemma-finite-type-over-affine-ample-very-ample, line 9539.
- morphisms-lemma-locally-projective-proper, line 10601.
- morphisms-lemma-nagata-normalization, line 14831.
- morphisms-lemma-normalization-normal, line 14651.
- morphisms-lemma-projective-is-quasi-projective-proper, line 10798.
- morphisms-lemma-projective-permanence, line 10845.
- morphisms-lemma-projective-quasi-projective, line 10707.
- morphisms-lemma-proper-local-on-the-base, line 9904.
- morphisms-lemma-pullback-ample-tensor-relatively-ample, line 8838.
- morphisms-lemma-quasi-affine-finite-type-over-S, line 9394.
- morphisms-lemma-quasi-compact-immersion, line 1139.
- morphisms-lemma-quasi-compact-scheme-theoretic-image, line 849.
- morphisms-lemma-quasi-projective-open-projective, line 10739.
- morphisms-lemma-scheme-theoretic-union, line 554.
- morphisms-lemma-ubiquity-nagata, line 3281.
- morphisms-proposition-generic-flatness, line 5181.
- morphisms-section-dimension-formula, line 13720.
- morphisms-section-generically-finite, line 13331.
- morphisms-section-nagata, line 3259.
- morphisms-section-normalization, line 14503.
- morphisms-section-projective, line 10501.
perfect.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 83bd632e693848d32b54acc48ea7d89b0ed024c4b84499486687e31e92bfdcf0; 417503 bytes.
pic.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 e6651e5453a362eb65096efa90a116188af3396425a2d3857e1648658823cc60; 65446 bytes.
preamble.tex
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 4af3f52ed0f1e932def5c8725068968407ce9e4b0cd4f4c4b803607b5bcbbe0d; 8596 bytes.
properties.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 2f8be43be8da39df575581181f8a28aaa077266464947157e70838462e8291fa; 213401 bytes.
- properties-definition-nagata, line 1632.
- properties-lemma-ample-on-closed, line 4386.
- properties-lemma-ample-power-ample, line 4372.
- properties-lemma-ample-quasi-coherent, line 5133.
- properties-lemma-characterize-regular, line 1141.
- properties-lemma-normal-dimension-2-Cohen-Macaulay, line 1596.
- properties-lemma-normal-integral-sections, line 1006.
- properties-lemma-regular-normal, line 1184.
quot.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 4949679b9a1b178ce7df1f3295cc3dedc5e8e141b9e1838db9766a5237690395; 237556 bytes.
resolve.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 4cc743f7c82f9c3845bb8c91447cb7adc27bdc3305fc2036eeddf41469320554; 202393 bytes.
- resolve-theorem-resolve, line 3945.
- resolve-lemma-resolve-complete, line 3834.
- resolve-lemma-rational-to-gorenstein, line 2471.
- resolve-lemma-resolve-rational-double-points, line 3499.
- resolve-lemma-contraction, line 4461.
- resolve-lemma-contract-ample, line 4666.
schemes.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 028a8204a03e736e9f22ff0d7c6444a17d04bfd5cdbbd31f4cdf322bec55f233; 189721 bytes.
- schemes-lemma-morphism-into-affine, line 885.
- schemes-proposition-characterize-universally-closed, line 4183.
- schemes-section-points, line 2512.
sites-cohomology.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 0d9e067d20f6a708bb228ec7b0f6da7881901c6c49cb38887553c17cd3a7b023; 534532 bytes.
spaces-cohomology.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 81438f655ceab1a2e07cfeec645a9a7c2447db983d6bcefaed6575859b75d196; 174442 bytes.
spaces-limits.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 63df4873f4d309a436ee8551a480a37805344fc377f1963376219f98d07bc228; 209790 bytes.
- spaces-limits-lemma-refined-valuative-criterion-proper, line 4888.
- spaces-limits-proposition-there-is-a-scheme-finite-over, line 3569.
spaces-more-morphisms.tex
Complete local source · exact pinned version
Role: native source comparator. SHA256 d739b3b42ce8590331c4dcf81c45d17a5f2430e46d03c004fef64034816c5081; 516999 bytes.
- Ordinary source comparator, not a substitute stable-moduli proof.
spaces-morphisms.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 048bc16d80e71dbaa9c5cf11b109b69b481d920b278cbcb379c3bc9b8bbfc252; 398512 bytes.
- spaces-morphisms-lemma-base-change-flat, line 5824.
- spaces-morphisms-lemma-base-change-proper, line 7916.
- spaces-morphisms-lemma-diagonal-unramified-morphism, line 7508.
- spaces-morphisms-lemma-equality-of-morphisms, line 3372.
- spaces-morphisms-lemma-etale-unramified, line 7831.
- spaces-morphisms-lemma-lift-valuation-ring-through-flat-morphism, line 8741.
- spaces-morphisms-lemma-push-down-solution, line 8304.
- spaces-morphisms-lemma-refined-valuative-criterion-universally-closed, line 8779.
stacks-more-morphisms.tex
Complete local source · exact pinned version
Role: native proof body. SHA256 38c2be1dc32b9fca7e819aabf1ad3c5067c6eab475f82bd61e5b8b3e12f7bbbc; 198225 bytes.
- stacks-more-morphisms-lemma-refined-valuative-criterion-proper, line 2692.
- stacks-more-morphisms-lemma-refined-valuative-criterion-separated, line 2803.
- stacks-more-morphisms-theorem-chow-finite-type, line 2242.
stacks-morphisms.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 1f81f01c6748709778c0f877f1cb687152b344aa1c455449d2a341bbfe6a8b90; 404259 bytes.
- stacks-morphisms-definition-fill-in-diagram, line 8848.
- stacks-morphisms-lemma-cat-dotted-arrows, line 8902.
- stacks-morphisms-lemma-cat-dotted-arrows-base-change, line 8974.
- stacks-morphisms-lemma-cat-dotted-arrows-independent, line 8938.
- stacks-morphisms-lemma-criterion-proper, line 9637.
- stacks-morphisms-lemma-fppf-open, line 5724.
- stacks-morphisms-lemma-gerbe-fppf, line 6074.
- stacks-morphisms-lemma-gerbe-isom-fppf, line 6216.
- stacks-morphisms-lemma-helper-diagonal, line 9330.
- stacks-morphisms-lemma-image-proper-is-proper, line 8482.
- stacks-morphisms-lemma-properties-diagonal, line 131.
- stacks-morphisms-lemma-section-immersion, line 618.
- stacks-morphisms-lemma-separated-implies-isom, line 1639.
stacks-project.cls
Complete local source · exact pinned version
Role: original build support, licence or provenance. SHA256 dbace0cb163b1b24f2816d89c547a3d487d51d59ede0303fad079e8ae3f93254; 60186 bytes.
stacks-properties.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 59d6b6df8f528ed5d3a68d9b9d74622e9b643f3622cc4d381bb46cc27a990016; 120421 bytes.
topology.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 38d2e107901be84fa1ead3587db2fbfc50589914d49db0ed5937c14d9b934f34; 245067 bytes.
varieties.tex
Complete local source · exact pinned version
Role: native dependency. SHA256 bb075fde0a9a393f3a15a5006ed9b755efc06050e746fd6113629bec0d92511a; 463806 bytes.
- varieties-definition-algebraic-scheme, line 3730.
- varieties-definition-degree-invertible-sheaf, line 9796.
- varieties-lemma-ample-curve, line 10253.
- varieties-lemma-ampleness-in-terms-of-degrees-components, line 10325.
- varieties-lemma-change-fields-pic, line 5840.
- varieties-lemma-check-invertible-sheaf-trivial, line 10190.
- varieties-lemma-degree-effective-Cartier-divisor, line 10088.
- varieties-lemma-degree-tensor-product, line 10039.
- varieties-lemma-dimension-fibre-in-higher-codimension, line 3681.
- varieties-lemma-dimension-locally-algebraic, line 3793.
- varieties-lemma-divisible, line 10127.
- varieties-lemma-euler-characteristic-additive, line 6227.
- varieties-lemma-finite-in-codim-1, line 3278.
- varieties-lemma-image-irreducible, line 1632.
- varieties-lemma-modification-normal-iso-over-codimension-1, line 3310.
- varieties-lemma-prepare-delta-invariant, line 9074.
- varieties-lemma-proper-geometrically-reduced-global-sections, line 1943.
- varieties-lemma-regular-functions-proper-variety, line 4908.
- varieties-lemma-smooth-separable-closed-points-dense, line 4671.
- varieties-lemma-variety-with-smooth-rational-point, line 4789.
- varieties-section-divisors-curves, line 9782.