Prerequisites

Result-level reading order and supporting-proof boundaries

Each lesson states its mathematical hypotheses and identifies the results it uses. The following referenced results are outside this selection; their appearance here does not supply a proof.

Spectral spaces and affine realization

AG-CA-01S. Referenced by AG-CA-01. Optional forward reading on spectral realization, not a prerequisite of the selected algebra arguments. This extra lesson is not included.

Principal standard étale form

AG-FSE-04, Section 3, Theorem 3.1 is included. It follows the preliminary AG-CA-17 results through Lemma 7.5, AG-CA-18 flatness and algebraic Zariski Main; it then supplies AG-CA-17 Theorem 7.6 and the henselian section criterion.

Dimension of fibres

AG-MO-11. Referenced by AG-MO-12. The Zariski Main introduction refers here for the local fibre-dimension convention. The selected pointwise quasi-finite criterion is fully stated in AG-MO-06 Theorem 1.1; this reference does not supply another proof in this collection.

Distinct bridge results

For any faithfully flat R -> S and any R-module M, if M tensor_R S is projective, then M is projective. No finite-generation assumption.
A separated, universally closed, locally finite-type morphism with finite fibres is finite, over an arbitrary base.
The nonaffine relative-integral-completion argument of Theorem 4.1, with its exact separated finite-type hypotheses over an arbitrary base.