1. • Formulation of the “hard comparison theorem”
   

    (former Bloch-Kato Conjecture).

1. • Current status of the proof of “hard comparison”

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.