Motivic Homotopy

Motivic Homotopy

(former Bloch-Kato Conjecture).

About: I have worked on problems related to the concept of mixed motives from 1990 to 2010. I am not actively working on this kind of problems now.

The last topic I worked on was the proof of a group of conjectures due to Quillen, Milnor, Bloch, Kato, Lichtenbaum and Beilinson which relate algebraic K-theories to the etale cohomology. A formulation of the key conjecture of this group and references to the papers with the proof can be found below.