Oliver Club

Kiran KedlayaUniversity of California, San Diego
Etale and crystalline companions

Friday, April 26, 2019 - 4:30pm
Malott 251

Consider a smooth variety $X$ over a finite field of characteristic $p$. In the context of his proof of the Weil conjectures, Deligne made a far-reaching conjecture about a certain category of $l$-adic sheaves on $X$. Under mild conditions, he conjectured such a sheaf belongs to a family of $l$-adic sheaves for all l different from $p$, as well as a then-mysterious member corresponding to $l = p$. We describe the missing object and the key ingredients in the proof of Deligne's conjecture. These include work of L. Lafforgue, T. Abe, a finiteness argument of Deligne, and an ingenious argument of Drinfeld.

Refreshments will be served at 4:00 PM in Malott 532.