University of Cambridge > Talks.cam > Number Theory Seminar > Counting Galois representations with Steinberg monodromy

Counting Galois representations with Steinberg monodromy

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Tom Fisher.

Let X be a smooth projective absolutely irreducible curve over Fq . Let S be a finite set of closed points of X of cardinality N > 1 . Put XS = X – S . Let pi1(XS) be the arithmetic fundamental group of the affine curve XS . It is Gal(FS/F) , where F is the function field of X over Fq and FS is the maximal extension of F unramified at each closed point of XS inside a fixed separable closure \ov{F} of F. We compute, in terms of the zeta function of X, the number of equivalence classes of irreducible n-dimensional ell-adic representations of pi1(XS), whose local monodromy at each point of S is a single Jordan block of rank n, assuming N is even if n = 2, that n is a prime and (n,q) = 1. This number is reduced to that of the nowhere ramified cuspidal automorphic representations of the multiplicative group of a division algebra of degree n over F, which we compute using the trace formula.

This talk is part of the Number Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity