On the structure of etale motivic cohomology

TL;DR

This paper explores the intricate structure of integral etale motivic cohomology groups across various types of schemes and fields, providing insights into their properties and relationships.

Contribution

It offers a detailed analysis of the structure of etale motivic cohomology groups for different classes of schemes over various fields, advancing understanding in algebraic geometry.

Findings

Characterization of cohomology group structures

Comparison across different base fields

Identification of key properties and invariants

Abstract

We discuss the structure of integral etale motivic cohomology groups of smooth and projective schemes over algebraically closed fields, finite fields, local fields, and arithmetic schemes.