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arXiv · 1409.4071

Geometric Eisenstein series: twisted setting

Sergey Lysenko
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Abstract

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the setting of the quantum geometric Langlands program (for \'etale l-adic sheaves) in analogy with [3]. We calculate the intersection cohomology sheaf on the version of Drinfeld compactification in our twisted setting. In the case G=SL_2 we derive some results about the Fourier coefficients of our Eisenstein series. In the case of G=SL_2 and X=P^1 we also construct the corresponding theta-sheaves and prove their Hecke property.

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Sergey Lysenko. 2014-09-14. Geometric Eisenstein series: twisted setting. https://arxiv.org/abs/1409.4071

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