Reading order

Collection contents

1. Read the selected commutative-algebra foundations at their stated hypotheses.
2. AG-CA-17 preliminary lifting results through Lemma 7.5 precede AG-CA-18 smooth-flatness and the flat-unramified criterion.
3. Algebraic Zariski Main, Theorem 1.1, uses the included conductor and strong-transcendence proofs.
4. AG-FSE-04 Theorem 3.1 proves principal standard étale form. It then supplies AG-CA-17 Theorem 7.6 and the henselian section criterion.
5. AG-FSE-07 Theorem 5.6 gives finite étale henselian-pair equivalence. AG-DFG-03 Theorem 6.4 then supplies integral descent for the argument in AG-FSE-07 Theorem 5.7.

AG-MO-06 Section 5, Theorem 5.1 is arbitrary-base Chevalley. Section 4 is the Noetherian version.

Supplementary AG-FSE-03 Sections 1–5 and Proposition 6.1 supply the written unramified core and monomorphism criterion. AG-FSE-06 Lemma 1.1, Section 5 (including Theorem 5.3) and Lemma 6.1 supply the lifting, thickening-equivalence and one-square-presentation results. The stronger 05A9, 02LS and 03GW obligations remain at their exact affected lesson boundaries. See the precise scope notes.

Selected full sources preserve their further named references. Sheaf and scheme foundations from Sheaves and schemes, as well as other explicitly referenced supporting results outside this finite collection, are not claimed as newly included or recursively re-audited.