Description

Number Theory Seminar

Monday, 23 October 2023, 14:30

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Venue: Ramanujan hall

Host: U. K. Anandavardhanan

Speaker: Anand Chitrao

Affiliation: TIFR Mumbai

Title: Reductions mod $p$ of semi-stable representations.

Abstract: We compute the reductions mod $p$ of irreducible two-dimensional semi-stable representations of the absolute Galois group $\GQp$ of $\Qp$. We use the compatibility with respect to reduction mod $p$ between the $p$-adic Local Langlands Correspondence and an Iwahori theoretic version of the mod $p$ Local Langlands Correspondence. By estimating certain logarithmic functions on $\Qp$ by polynomials on open subsets of $\Zp$, we compute the reductions mod $p$ completely for weights at most $p + 1$. We also state how this method can be used, in theory, to compute the reductions mod $p$ of semi-stable representations of arbitrarily large weights. In passing, we extend some results on Iwahori induction to the case of non-commutative Hecke algebras.

Description

Ramanujan Hall, Department of Mathematics

Date

Mon, October 23, 2023

Start Time

2:30pm IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, October 23, 2023 10:47am IST