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.
Idea of the proofMy idea of how to prove Gersten's conjecture has come from weight argument of Adams operations in [GS87] and [GS99]. In my viewpoint, difficulty of solving Gersten's conjecture consists of ring theoretic side and homotopy theoretic side. We will explain ideas about how to overcome each difficulty.