A survey of Gersten's conjecture

TL;DR

This paper surveys Gersten's conjecture, discussing its background, significance, and recent developments, including the author's own work on the motivic version of the conjecture.

Contribution

It provides a comprehensive overview of Gersten's conjecture and introduces new insights into the motivic version based on the author's recent research.

Findings

Summarizes key results and open problems related to Gersten's conjecture.

Introduces the author's recent work on motivic Gersten's conjecture.

Highlights the importance of the conjecture in algebraic K-theory and motivic homotopy theory.

Abstract

This article is the extended notes of my survey talk of Gersten's conjecture given at the workshop "Bousfield classes form a set: a workshop in a memory of Tetsusuke Ohkawa" at Nagoya University in August 2015. In the last section, I give an explanation of my recent work of motivic Gernsten's conjecture.