Spring School on higher dimensional class field theory

Organizers:

• Moritz Kerz (Essen)
• Stefan Müller-Stach (Mainz)

Speakers and Titles

• Ralf Gerkmann (München): Introduction to class field theory (Lecture notes)
  
• Tamas Szamuely (Budapest): Wiesend's higher class field theory
• Alexander Schmidt (Heidelberg): Wiesend's covering construction and ramification theory
• Uwe Jannsen (Regensburg): Hasse principles from Brauer to Kato I
  
• Shuji Saito (Tokyo): Hasse principles from Brauer to Kato II
  
  

The goal of this workshop is to give an introduction to recent progress on the class field theory of higher dimensional arithmetic schemes and on higher dimensional Hasse principles. The lectures will assume only a basic acquaintance with classical class field theory and some knowledge of algebraic geometry.

Ralf Gerkmann will recall classical results from class field theory of local and global fields.

Alexander Schmidt and Tamas Szamuely will describe a new approach to the higher dimensional reciprocity isomorphism originating in the work of Goetz Wiesend. The reciprocity isomorphism describes the abelian fundamental group of an arithmetic scheme in terms of some idelic data, namely the class group of the scheme. An example of a higher dimensional class group is given by the Chow group of zero cycles if the scheme is proper over the integers.

Uwe Jannsen will explain Kato's conjectures on higher cohomological Hasse principles. These conjectures generalize the classical Brauer-Hasse-Noether theorem about the Brauer group of a number field. There has been a lot of progress towards a proof of these conjectures during the last twenty years and in his talks Jannsen will explain the role of etale homology and the Weil conjectures.

Provisional Schedule

Registration: Monday 9 am, room 05-432 (Hilbertraum)

Conference dinner: Tuesday, 7 p.m., Proviant-Magazin, Schillerstr. 11a, Mainz

Travel information

All lectures will take place in the Mathematics Department of the University of Mainz, Staudinger Weg 9, in room 05-514. Here is a map of the campus. The closest airport is located at Frankfurt/Main. Find your way from the airport to the institute here.