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

## Counting Galois representations with Steinberg monodromyAdd to your list(s) Download to your calendar using vCal - Yuval Flicker (Ohio)
- Tuesday 24 March 2009, 14:30-15:30
- MR13.
If you have a question about this talk, please contact Tom Fisher. Let S be a finite set of closed points of X of cardinality N > 1 . Put X . Let ^{S} = X – Spi be the arithmetic fundamental group of the affine curve _{1}(X^{S})X . It is ^{S}Gal(F , where ^{S}/F)F is the function field of X over and F_{q}F is the maximal extension of ^{S}F unramified at each closed point of X inside a fixed separable closure \ov{F} of ^{S}F. We compute, in terms of the zeta function of X, the number of equivalence classes of irreducible n-dimensional ell-adic representations of pi, whose local monodromy at each point of _{1}(X^{S})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. ## This talk is included in these lists:- All CMS events
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