Speaker: Sabyasachi Dhar, IIT Kanpur

Date & Time: Thursday, 30 January 2025, 5 pm

Meet Link: meet.google.com/wqq-hjhc-fqc

Title: Tate cohomology and base change for generic representations of GL(n)

Abstract: Principle of functoriality is a central problem in Langlands
program, proposed by R. P. Langlands. D. Treumann and A. Venkatesh in their
foundational work established a functoriality lifting of mod-l Hecke
eigenclasses of H to the mod-l Hecke eigenclasses of G, where G is a
connected reductive algebraic group defined over a number field, and H is
the connected component of the fixed points of G under an automorphism T of
G of prime order l. They made some conjectures for representation theory of
p-adic groups which predict that the functoriality for local
representations is realized via Tate cohomology under the action of the
cyclic group generated by T. In this talk, we discuss the conjecture in the
context of local cyclic base change for generic representations of the
general linear group GL(n,F), where F is a finite extension of the field of
p-adic numbers.