Wintersemester 2009/2010 :

A1-homotopy theory and the Friedlander-Milnor conjecture (4 hours). Mo, Do 10-12, HS B 045. Ueb., Di 10-12, Zimmer C 113.

In this lecture we intend to give a detailled account of our proof of the Friedlander conjecture. In the first part we will prove all the basic results concerning the structure of A^1-homotopy and A^1-homology sheaves, and on the singular simplicial construction on sheaves. The second part will explain the proof of the conjecture. This lecture is a sequel of the course ``A1-homotopy theory" of the previous semester. The ``Uebungen" will be a series of complements to the lecture.
The Bloch-Kato conjecture (II), after Rost and Voevodsky (2 hours). Di 16-18, HS B 134.

This Lecture is the second part of a series of lectures aimed at explaining the proof of the Bloch-Kato conjecture, following Rost and Voevodsky. We will explain the general strategy of the proof, due to Voevodsky, which reduces the Bloch-Kato conjecture to the construction of ``nice" Norm Varieties for each Symbol. We will use the construction of the Steenrod operations given in the course ``A1-homotopy theory" of the last summersemester. The end of the proof will be probably given in the Fall 2010, especially the inductive construction of the required nice Norm Varieties, and their basic correspondence, due to Rost.