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تسجيل مستخدم جديدParabolic Hecke eigensheaves
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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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The aim of these notes is to generalize Laumons construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve $C$ to the case of local systems with indecomposable unipotent ramification at a finite set of point
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We continue to develop the analytic Langlands program for curves over local fields initiated in arXiv:1908.09677, arXiv:2103.01509 following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators introduced in arXiv:21
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