Sources and component terms
The independently written lessons use CC0 1.0. Quotients and torsors incorporates the Stacks proofs identified in its source and uses GNU FDL 1.2 or later, with no Invariant Sections or Cover Texts. Its source copyright, history and complete licence remain attached.
Human references and AI authorship are stated in each lesson and prerequisite reading. Mathematical comparison is distinct from reuse of source expression.
MathJax uses Apache 2.0; font notices accompany the reader.
The six normalization-transfer proofs and the nine arbitrary-base integral-effectivity results in Quotients and torsors, Appendices E–F, are independently expressed under CC0 1.0. Existing incorporated material retains its stated terms.
The eleven field-family prerequisites in Quotients and torsors, Appendix G, and the original reproducible Picard-family diagram are independently expressed under CC0 1.0. Existing incorporated material retains its stated terms.
The thirty normalization, analytic helper, component and ampleness results in Quotients and torsors, Appendices H–I, and their three reproducible schematics are independently expressed under CC0 1.0. Existing incorporated material retains its stated terms.
Companion components
The companion readings retain their stated authorship and component terms. Complete editable sources, native excerpts and source notices accompany them.
- Complex analytic spaces and analytification: CC0-1.0 AND LicenseRef-Demailly-OpenContent
- Local tools for bundles and transport: CC0-1.0 AND CC-BY-SA-4.0
- Laurent series and homogeneous projections: CC-BY-SA-4.0
- The complex exponential and the circle: CC-BY-SA-4.0
- Real analysis on closed intervals: CC-BY-SA-4.0
- Dimension theory of Noetherian local rings: GFDL-1.2-or-later
- Constructing the real numbers: CC-BY-4.0
- Krull dimension and Noether normalization: GFDL-1.2-or-later
- Tor and flat modules: GFDL-1.2-or-later
- Formally smooth, unramified and étale ring maps: CC0-1.0
- Faithful flatness and the local criterion for flatness: CC0-1.0
- Resolutions, Tor and Ext: CC0-1.0
- Kähler differentials: GFDL-1.2-or-later
- Projective dimension and the Auslander–Buchsbaum formula: CC0-1.0
- Regular local rings: CC0-1.0
- Étale morphisms and their local structure: CC0-1.0
- Zariski's Main Theorem: CC0-1.0
- Regular sequences, depth and Cohen–Macaulay modules: GFDL-1.2-or-later
- Dimension theory of Noetherian local rings: GFDL-1.2-or-later
- Smooth algebras over a field and the Jacobian criterion: CC0-1.0
- Quasi-finite morphisms and Chevalley’s theorem: CC0-1.0
- Affine morphisms, relative Spec, and finite morphisms: CC0-1.0
- Limits of schemes and Noetherian approximation: CC0-1.0
- Finiteness of morphisms: CC0-1.0
- The diagonal and separated morphisms: CC0-1.0
- Normalization: CC0-1.0
- The Killing form and Cartan's criteria: CC0-1.0
- Nilpotent and solvable Lie algebras: Engel's and Lie's theorems: CC0-1.0
The new independently written explanations and proofs on geometric quotients, integral affine-neighbourhood descent and supplied foundations are dedicated to CC0 1.0. Existing incorporated components retain their attached terms and notices.
Projected companion MathJax runtimes retain their Apache 2.0 terms and byte-identical notices: