Abstract for the seminar talk on 22.02.2008

Dr. Egon Rütsche (ETH Zurich)
Adelic Openness for Drinfeld modules in generic characteristic
Time: 14.15 / Place: HWZ (HG G43)

Let F be a finitely generated field of transcendence degree 1 over a finite field, and let A be the ring of all  elements of F which are integral outside a fixed place. We consider a Drinfeld A-module over a function field  of generic characteristic. For any prime of A, we have a continuous Galois representation on the Tate module  of the Drinfeld module. If we take the product of these representations over all primes of A, we get the so-called adelic representation. If the absolute endomorphism ring of the Drinfeld module is equal to A, we prove that the image of the adelic representation is open. This is an analogue of Serre's result for elliptic curves without potential complex multiplication.