Geodesic
Geometric Eisenstein series: twisted setting
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 3179-3252 Cet article a éte moissonné depuis la source EMS Press

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Let G be a simple simply-connected group over an algebraically closed field k, and X a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack BunG​ of G-torsors on X in the setting of the quantum geometric Langlands program (for étale Ql​-sheaves) in analogy with [3]. We calculate the intersection cohomology sheaf on the version of Drinfeld compactification in our twisted setting. In the case of G = SL2​ we derive some results about the Fourier coefficients of our Eisenstein series. For G = SL2​ and X=P1 we also construct the corresponding theta-sheaves and prove their Hecke property.
DOI : 10.4171/jems/738
Classification : 11-XX, 14-XX
Keywords: Geometric Langlands program, Brylinski–Deligne extensions, covering groups, quantum geometric Langlands program, Eisenstein series 
@article{JEMS_2017_19_10_a8,
     author = {Sergey Lysenko},
     title = {Geometric {Eisenstein} series: twisted setting},
     journal = {Journal of the European Mathematical Society},
     pages = {3179--3252},
     year = {2017},
     volume = {19},
     number = {10},
     doi = {10.4171/jems/738},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/738/}
}
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Sergey Lysenko. Geometric Eisenstein series: twisted setting. Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 3179-3252. doi: 10.4171/jems/738

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