100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Thierry Gallay

Richard Crew

p-adic local systems
Jeudi, 17 Mai, 2018 - 10:30
Résumé : 

Picard and Fuchs observed long ago that the periods of integrals on a family of algebraic varieties are solutions of differential equations. The modern version of this is the Gauss-Manin connection on the relative de Rham cohomology of the family. In an arithmetic setting the formal horizontal sections of this connection have good p-adic convergence properties for most primes. I will describe a proof of this using Berthelot's theory of arithmetic D-modules, and then show how one can construct arithmetic differential operator rings for families with singularites.

Institution de l'orateur : 
University of Florida (USA)
Thème de recherche : 
Théorie des nombres
Salle : 
Salle 4
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