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l-adic local systems over a curve

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  • UserHongjie Yu (IMJ-PRG)
  • ClockTuesday 16 October 2018, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Beth Romano.

Let X_1 be a projective, smooth and geometrically connected curve over F_q, and let X be its base change to an algebraic closure of F_q. The Frobenius element permutes the set of isomorphism classes of irreducible l-adic local systems with a fixed rank on X. In 1981, Drinfeld has calculated the number of fixed points of this permutation in the rank 2 case. Curiously, it looks like the number of F_q-points of a variety defined over F_q. In this talk, we generalize Drinfeld’s result to higher rank case. Our method is purely automorphic, in fact we do that by using Arthur-Lafforgue’s trace formula.

This talk is part of the Number Theory Seminar series.

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