Title: mod $p$ local Langlands correspondence for $GL_2$
Speaker: Mihir Sheth (IISc Mathematics)
Date: 03 September 2021
Time: 2 pm
Venue: Microsoft Teams (Online)
Let $F$ be a non-archimedean local field of residue characteristic $p$. The classical local Langlands correspondence is a 1-1 correspondence between 2-dimensional irreducible complex representations of the Weil group of $F$ and certain smooth irreducible complex representations of $GL_2(F)$. The number-theoretic applications made it necessary to seek such correspondence of representations on vector spaces over a field of characteristic $p$. In this talk, however, I will show that for $F$ of residue degree $> 1$, unfortunately, there is no such 1-1 mod $p$ correspondence. This result is an elaboration of the arguments of Breuil and Paskunas to an arbitrary local field of residue degree $> 1$.