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Summer School on p-adic Cohomology

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The aim of this summer school is to give a survey on recent developments in p-adic cohomology, covering both theoretical and computational aspects. It is also intended to serve as an introduction into this area for PhD students and interested researchers. The summer school is organized by the members of the SFB/TR 45 and financed by the Deutsche Forschungsgemeinschaft.

What
  • Summer School
When Sep 29, 2008 09:00 AM to
Oct 02, 2008 05:00 PM
Where Department of Mathematics, University of Mainz
Contact Name
Contact Phone +49 6131 3923609
Attendees PhD students and interested researchers
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Speakers

Pierre Berthelot
(Universite de Rennes):
"Introduction to  arithmetic D-modules"
Richard Crew
(University of Florida):
"The monodromy theorem in p-adic cohomology"
Kiran Kedlaya
(Massachusetts Institute of Technology):
"Effective methods in p-adic cohomology"

 

(Titles are preliminary)

 

Program

 

Kiran Kedlaya's course will focus on comparisons between rigid cohomology and algebraic de Rham cohomology, both for individual varieties and for families of varieties. In the latter case, we will use some basic properties of p-adic differential equations. The aim is to provide tools needed to carry out effective computations, e.g., of zeta functions of varieties.

Richard Crew's lectures will be centered around the notion of overconvergent F-isocrystals and their monodromy groups, leading up to the p-adic monodromy theorem. Pierre Berthelot's course will provide an introduction to arithmetic D-modules. Conjecturally, these form a suitable category of coefficients for rigid cohomology. They are also an important tool for the derivation of structural results, e.g. the finite-dimensionality of cohomology spaces.

A detailed schedule can be found here.

 

Prerequisites

We assume the usual background in algebraic and complex geometry, as covered e.g. by Hartshorne's and Voisin's books. Some familiarity with the basic theory of complete non-archimedian fields will also be helpful.

 

List of Participants

A list of participants is available here.

 

Applications and Financial Support

Full financial support is available for members of the SFB/TR 45. There is limited support for other participants, too. Please indicate in the application form if you would like us to reserve a hotel room for you. During the summer school, lunch can be taken at the Zentralmensa (student cafeteria), which is close to the institute.

 

Travel information

All lectures will take place in the Mathematics Department of the University of Mainz, Staudinger Weg 9, in room 05-426. 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.

 

Further information

If you have additional questions, please contact the organizers.

  • Duco van Straten (straten@mathematik.uni-mainz.de)
  • Ralf Gerkmann (gerkmann@mathematik.uni-mainz.de)
  • Kira Samol (samol@mathematik.uni-mainz.de)