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Penn Mathematics Colloquium

Wednesday, March 13, 2019 - 3:30pm

Kiran Kedlaya



University of Pennsylvania


Tea will be served at 3:00 in DRL 4E17

Let X be a smooth variety (e.g., affine space) over a finite field
(e.g., the integers modulo a prime). In the course of proving the last
of Weil's conjectures on zeta functions of varieties over finite field,
Deligne studied a certain category of representations of the fundamental
group of X which carry information about these zeta functions. He also
made a far-reaching conjecture to the effect that such objects always
look as if they "come from geometry".

We will state the conjecture, describe some of its more concrete consequences, and discuss some
results of various authors (L. Lafforgue, V. Lafforgue, Deligne,
Drinfeld, T. Abe, Abe-Esnault, and the speaker) which very recently have
led to a resolution of this 40-year-old open problem.