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SUMMARY:l-adic local systems over a curve - Hongjie Yu (IMJ-PRG)
DTSTART:20181016T133000Z
DTEND:20181016T143000Z
UID:TALK110293@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:Let X_1 be a projective\, smooth and geometrically connected c
 urve over F_q\, and let X be its base change to an algebraic closure of F_
 q.\nThe Frobenius element permutes the set of isomorphism classes of irred
 ucible 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 c
 ase. Curiously\, it looks like the number of F_q-points of a variety defin
 ed 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 Arth
 ur-Lafforgue's trace formula.
LOCATION:MR13
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