Algebra and Number Theory Seminar: Kirti Joshi

Title: Anabelomorphy and the local Langlands Correspondence.

 

Abstract:  Anabelomorphy is a notion I formulated to formalize Mochizuki's ideas about anabelian way of changing base rings. In the concrete context of p-adic fields this means understanding arithmetic while keeping the absolute Galois group of a p-adic field fixed, but not fixing the field. Since the Local Langlands correspondence deals with representations of Galois (or more precisely Weil-Deligne) group, one may ask: To what extent is the p-adic field K tied to the representation theory of topological groups appearing in the Local Langlands Correspondence. My results are quite unexpected and my talk will be a panorama of some of the results obtained to date.