The Tate module of Deligne's 1 motive and class groups as Galois modules
Speaker: Professor Cornelius Greither (Universitaet der Bundeswehr Muenchen)
Date: Wed 25th November 2009
Location: Mathematical Sciences Seminar Room
We consider a G-Galois covering XoY 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 fZell-module with action of G and Frobenius. It is closely linked to the ell-part of the class group of arX (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.)