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Drinfeld's work on the pro-semisimple completion of the fundamental group of a smooth variety over a finite field

Hot Topics: Recent progress in Langlands Program April 08, 2019 - April 12, 2019

April 12, 2019 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Stefan Patrikis (University of Utah)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Langlands correspondence

  • independence-of-l

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

19-Patrikis

Abstract

The l-adic pro-semisimple completion of a profinite group packages its l-adic representations valued in (not necessarily connected) semisimple groups. When the profinite group considered is the étale fundamental group of a smooth variety over a finite field k, Drinfeld has proven an "independence-of-l" result for these pro-semisimple completions. This talk will describe the result precisely, and explain how Drinfeld ultimately reduces it to the existence of compatible systems containing a given l-adic local system on X. This existence result in turn follows from the Langlands correspondence when X is a curve, and in general from an earlier result of Drinfeld reducing the general case to the case of curves.

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Video/Audio Files

19-Patrikis

H.264 Video 855_26575_7723_19-Patrikis.mp4
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