Workshop: Cohomological Hasse principle (WS 2011/12)

In 1985 K. Kato formulated a fascinating framework of conjectures which generalize the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for arithmetic schemes, that is schemes of finite type over a finite field or over the ring of integers in a number field or a local field. The conjecture plays a significant role in arithmetic geometry. There is work on special cases of this conjecture by Kato, Colliot-Thelene and Jannsen-Saito. Recently, in [J] and [JS], general approaches are proposed to solve the Kato conjecture for schemes over a finite field assuming the resolution of singularities. Based on these results, in [KS] Kerz and Saito proved the conjecture in the prime-to-characteristic case under weaker assumptions, using refined alterations due to Gabber.

The goal of this workshop is to study the work of Jannsen, Kerz and Saito and some of its applications to higher Chow groups of arithmetic schemes, higher class field theory, and special values of zeta functions.

[J] U. Jannsen, Hasse principles for higher dimensional fields, arXiv:0910.2803v1

[JS] U. Jannsen, S. Saito, Kato conjecture and motivic cohomology over finite fields, arXiv:0910.2815v1

[KS] M. Kerz, S. Saito, Cohomological Hasse principle and motivic cohomology for arithmetic schemes, arXiv:1010.5930v1

Below you find a detailed program.

Programm (pdf)

The proposed dates for the workshop are three Saturdays (12.11.2011, 10.12.2011, 14.1.2012) at different universities.

1st meeting: 12.11.2011, Essen

Talk 1: Ralf Kasprowitz
Talk 2: Alexander Ivanov
Talk 3: Kai Rülling
Talk 4: Ulrich Görtz

2nd meeting: 10.12.2011, Düsseldorf

Talk 1: Timo Richarz
Talk 2: Jochen Heinloth
Talk 3: 
Talk 4: Christian Liedtke

3rd meeting: 14.01.2012, Paderborn

Talk 1: Daniel Wortmann
Talk 2: Torsten Wedhorn/Yarek Yatsyshyn
Talk 3: Christian Kappen
Talk 4: Timo Keller

Organisatoren
Ulrich Görtz (ulrich.goertz@uni-due.de)
Ralf Kasprowitz (kasprowi@math.uni-paderborn.de)
Torsten Wedhorn (wedhorn@math.uni-paderborn.de)