The Bloch-Ogus Theorem over DVR

TL;DR

This paper proves the Bloch-Ogus Theorem for regular local rings over a discrete valuation ring, including those of mixed characteristic that are essentially smooth, expanding its applicability.

Contribution

It extends the Bloch-Ogus Theorem to regular local rings of mixed characteristic that are essentially smooth over a DVR.

Findings

Proves Bloch-Ogus Theorem for regular local rings over DVRs.

Establishes the theorem for rings of mixed characteristic that are essentially smooth.

Enhances understanding of cohomological properties of regular local rings.

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.