On a theorem of Narasimhan and Ramanan on deformations

2025/06/21 by Balaji, V., Pandey, Y. · 1 citation
#14D20 #14D23 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17574

Abstract

Let X be a smooth projective curve genus at least 3, over an algebraically closed field k of arbitrary characteristics. Let \cM denote the moduli stack \cM_X(\cH) of \cH-torsors on X, when \cH \em quasi-split absolutely simple, simply connected connected group scheme. Using the theory of parahoric torsors and Hecke correspondences, we describe the cohomology groups Hⁱ(\cM, \cT__\cM), i = 0,1,2 and Hⁱ(\cM, Ω__\cM), i = 0,1,2 in terms of the curve X. The classical results of Narasimhan and Ramanan are derived as a consequence.

Citations

• Etale Fundamental group of moduli of torsors under Bruhat-Tits group scheme over a curve
• Geometric Langlands Correspondence Near Opers
• Poincaré families of G-bundles on a curve
• Twisted loop groups and their affine flag varieties
• The strong Macdonald conjecture and Hodge theory on the Loop Grassmannian

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• Conformal blocks, parahoric torsors and Borel-Weil-Bott

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