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The Bloch-Ogus Theorem over DVR

Ivan Gaidai-Turlov

Abstract

We prove the Bloch-Ogus Theorem for regular local rings geometrically regular over a discrete valuation ring. In particular, we prove the Bloch-Ogus Theorem for regular local rings of mixed characteristic that are essentially smooth over a discrete valuation ring.

The Bloch-Ogus Theorem over DVR

Abstract

We prove the Bloch-Ogus Theorem for regular local rings geometrically regular over a discrete valuation ring. In particular, we prove the Bloch-Ogus Theorem for regular local rings of mixed characteristic that are essentially smooth over a discrete valuation ring.

Paper Structure

This paper contains 6 sections, 24 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Reduction to the case of the perfect infinite residue field
  4. The geometric case
  5. The general case
  6. Lindel--Ojanguren--Gabber’s lemma over a DVR

Key Result

Theorem 1. 1

Let $S$ be a regular local ring (possibly of mixed characteristic), geometrically regular over some discrete valuation ring $R$ with residue field $k$. Let $p = \operatorname{char} k$, and let $\Lambda$ be a finite $r$-torsion $\operatorname{Gal}(R)$-module with $p \nmid r$. Let $U = \mathop{\mathrm

Theorems & Definitions (24)

  • Theorem 1. 1
  • Lemma 2. 1
  • Lemma 2. 2
  • Lemma 3. 1
  • Lemma 3. 2
  • Lemma 3. 3
  • Lemma 3. 4
  • Lemma 4. 1
  • Lemma 4. 2
  • Lemma 4. 3
  • ...and 14 more