Professor Cornelius Greither (Universitaet der Bundeswehr Muenchen)

will speak on

The Tate module of Deligne's 1 motive and class groups as Galois modules

Time: 3:00PM
Date: Wed 25th November 2009
Location: Mathematical Sciences Seminar Room [map]

Abstract: We consider a $G$-Galois covering $X o Y$ of curves over a finite field. Deligne defined a certain 1-motive in this context (it is not necessary to know anything about motives for this talk!), and the $ell$-adic Tate module $M$ of this motive is a finitely generated free ${f Z}_ell$-module with action of $G$ and Frobenius. It is closely linked to the $ell$-part of the class group of $ar X$ (the curve $X$ base-changed to the algebraic closure of the base field), but it behaves better algebraically. In ongoing joint work, Popescu and I study $M$ as a Galois module. Applications include the calculation of Fitting invariants of class groups of curves, and an a priori lower bound on class groups of some Fermat curves.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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