Mathematics Seminar
Date: Thursday, June 30, 2022
Time: 3:30 pm to 4:30 pm
Venue: Online, via Zoom
The failure of a 1-1 mod p local Langlands correspondence for GL_2
Mihir Sheth
IISc, Bangalore.
30-06-22

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Abstract

Let F be a non-archimedean local field of residue characteristic p. The classical local Langlands correspondence gives a canonical bijection between smooth irreducible 2-dimensional complex representations of the Weil group of F and smooth irreducible supercuspidal complex representations of GL_2(F). Vigneras shows that such a canonical bijection exists for representations over any algebraically closed field of characteristic not equal to p. Building on the work of Breuil and Paskunas, I will show that this is no longer true for mod p representations when F has residue degree > 1.