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A C_2-equivariant Gabber presentation lemma

Tom Bachmann

Abstract

We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2.

A C_2-equivariant Gabber presentation lemma

Abstract

We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2.
Paper Structure (3 sections, 5 theorems, 4 equations)

This paper contains 3 sections, 5 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. Presentation lemma
  3. Applications

Key Result

Theorem 2.1

Let $k$ be an infinite field of characteristic $\ne 2$. Let $X$ be a smooth $k$-scheme with an action by $C_2$. Let $Z \subset X$ be a closed invariant subscheme of positive codimension and $z \in Z$ be a point (not necessarily closed). Then there exist: Moreover the following hold:

Theorems & Definitions (12)

  • Theorem 2.1
  • Remark 2.2
  • Remark 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • proof : Proof of Theorem \ref{['thm:main']}.
  • Lemma 3.1
  • proof
  • ...and 2 more