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arXiv · 1910.02357

Parabolic Hecke eigensheaves

Ron Donagi·Tony Pantev
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Abstract

We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line $C$ with tame ramification at five points $\{p_{1}, p_{2}, p_{3}, p_{4}, p_{5} \}$. In particular we construct the automorphic $D$-modules predicted by GLC on the moduli space of rank two parabolic bundles on $(C, \{p_{1}, p_{2}, p_{3}, p_{4}, p_{5} \})$. The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers of the Hitchin fibration to reduce the problem to one in classical projective geometry on the intersection of two quadrics in $\mathbb{P}^{4}$.

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Ron Donagi, Tony Pantev. 2019-10-06. Parabolic Hecke eigensheaves. https://arxiv.org/abs/1910.02357

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