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Intersection theory on non-archimedean analytic spaces

Yulin Cai

Abstract

We develop the intersection theory of non-archimedean analytic spaces and prove the projection formula and the GAGA principle. As an application, we naturally define the category of finite correspondences of analytic spaces.

Intersection theory on non-archimedean analytic spaces

Abstract

We develop the intersection theory of non-archimedean analytic spaces and prove the projection formula and the GAGA principle. As an application, we naturally define the category of finite correspondences of analytic spaces.
Paper Structure (23 sections, 39 theorems, 98 equations)

This paper contains 23 sections, 39 theorems, 98 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Support of a coherent sheaf
  4. Zariski image of a morphism
  5. Codimension
  6. A key lemma
  7. Meromorphic functions and Cartier divisors
  8. Meromorphic functions
  9. Cartier divisors
  10. Inverse image of a Cartier divisor
  11. Cycles, flat pull-backs and proper push-forwards
  12. Cycles
  13. Cycle associated to a coherent sheaf
  14. Weil divisors
  15. Flat pull-backs
  16. ...and 8 more sections

Key Result

Proposition 1.1

Let \xymatrix{Y'\ar[r]^{g'}\ar[d]_{f'}& Y \ar[d]^{f}\\ X'\ar[r]_{g}& X}be a Cartesian diagram of separated, strictly $K$-analytic spaces. Assume that $f$ is proper, and that $g$ is flat, has of relative dimension $r$. Then $f'$ is proper, $g'$ is flat and has relative dimension $r$. Moreover, $g^*

Theorems & Definitions (125)

  • Proposition 1.1: \ref{['prop:flatbasechangeofcycles']}
  • Theorem 1.2: Projection formula
  • Definition 2.1
  • Remark 2.2
  • Remark 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Proposition 2.6
  • ...and 115 more