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Quotients Of Admissible Formal Schemes and Adic Spaces by Finite Groups

Bogdan Zavyalov

Abstract

In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally strongly noetherian adic space.

Quotients Of Admissible Formal Schemes and Adic Spaces by Finite Groups

Abstract

In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally strongly noetherian adic space.

Paper Structure

This paper contains 37 sections, 97 theorems, 146 equations.

Table of Contents

  1. Introduction
  2. Overview
  3. Scheme Case
  4. Formal Schemes and Adic Spaces
  5. Generality
  6. Comparison with Han
  7. Our results
  8. Quotients of Schemes
  9. Review of Classical Theory
  10. Schemes Over a Valuation Ring $k^+$
  11. Quotients of Admissible Formal Schemes
  12. The Setup and the Candidate Space $\mathfrak X/G$
  13. Affine Case
  14. General Case
  15. Comparison between the schematic and formal quotients
  16. ...and 22 more sections

Key Result

Lemma 1.1.1

AM Let $R$ be a noetherian ring, and $B\subset C$ an inclusion of $R$-algebras. Suppose that $C$ is a finite type $R$-algebra, and $C$ is a finite $B$-module. Then $B$ is finitely generated over $R$.

Theorems & Definitions (268)

  • Lemma 1.1.1
  • Example 1.1.2
  • Theorem 1.3.1
  • Theorem 1.3.2
  • Theorem 1.3.3
  • Lemma 1.3.4
  • Remark 1.3.5
  • Theorem 1.3.6
  • Definition 2.1.1
  • Lemma 2.1.2
  • ...and 258 more