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On Liu morphisms in non-Archimedean geometry

Mingchen Xia

Abstract

We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly as affine morphisms and quasi-affine morphisms of schemes.

On Liu morphisms in non-Archimedean geometry

Abstract

We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly as affine morphisms and quasi-affine morphisms of schemes.

Paper Structure

This paper contains 22 sections, 44 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Main results
  4. Structure of the paper
  5. Conventions
  6. Acknowledgments
  7. Preliminaries
  8. Analytic spaces
  9. A representability theorem
  10. Polyradii
  11. The category of Banach modules
  12. Liu spaces and Liu algebras
  13. Liu spaces
  14. Liu algebras
  15. Coherent sheaves on Liu $k$-analytic spaces
  16. ...and 7 more sections

Key Result

Theorem 1.1

Let $X$ be a separated $k$-analytic space. Then the functor is an anti-equivalence of categories.

Theorems & Definitions (100)

  • Definition 1.1: c.f. \ref{['def:Liuspace']}
  • Definition 1.2: c.f. \ref{['def:quasiLiumor']}
  • Theorem 1.1: =\ref{['cor:Liuequivalence']}
  • Theorem 2.1
  • proof
  • Definition 2.1
  • Definition 2.2
  • Proposition 2.2: Berk12
  • Definition 3.1: MP21
  • Example 3.1
  • ...and 90 more