Lecture Announcement
Date: Wednesday, 30 July 2025
Time: 11:30 AM
Venue: Seminar Hall
On a theorem of Narasimhan-Ramanan on deformations of moduli stacks
V. Balaji
Chennai Mathematical Institute.
30-07-25

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Abstract

Let $X$ be a smooth projective curve over $k$ of genus at least $3$ and let $G$ be an {\em almost simple, simply-connected} connected group scheme over $k$. Let $\cM$ denote the moduli stack $\cM_X(G)$ of principal $G$-bundles on $X$. Using the theory of parahoric torsors and Hecke correspondences, we describe the cohomology groups $\text{H}^i(\cM, \cT_{_{\cM}}), i = 0,1,2$ and $\text{H}^i(\cM, \Omega_{_{\cM}}), i = 0,1,2$ in terms of the curve $X$. The classical results of Narasimhan and Ramanan are derived as a consequence.