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Adequate moduli spaces and geometrically reductive group schemes

Jarod Alper

Abstract

We develop the theory of adequate moduli spaces in characteristic $p$ (and mixed characteristic) characterizing quotients by geometrically reductive group schemes.

Adequate moduli spaces and geometrically reductive group schemes

Abstract

We develop the theory of adequate moduli spaces in characteristic (and mixed characteristic) characterizing quotients by geometrically reductive group schemes.

Paper Structure

This paper contains 40 sections, 61 theorems, 53 equations.

Table of Contents

  1. Introduction
  2. Conventions
  3. $G$-$R$-modules and algebras
  4. Locally nilpotent ideals
  5. Symmetric products
  6. Adequacy for rings
  7. Adequate ring homomorphisms
  8. Universally adequate ring homomorphisms
  9. Adequate homeomorphisms
  10. Universally adequate $\mathcal{O}_{\mathcal{X}}$-algebra homomorphisms
  11. Adequately affine morphisms
  12. The definition and equivalences
  13. Properties of adequately affine morphisms
  14. Generalization of Serre's criterion
  15. Adequate moduli spaces
  16. ...and 25 more sections

Key Result

Theorem 1

If $\mathcal{X}$ is an algebraic stack with quasi-finite and separated diagonal, the following are equivalent:

Theorems & Definitions (167)

  • Definition
  • Theorem
  • Definition
  • Theorem
  • Theorem
  • Theorem
  • Lemma 2.3.1
  • proof
  • Definition 3.1.1
  • Lemma 3.1.2
  • ...and 157 more