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Nearby cycles of Whittaker sheaves on Drinfeld’s compactification

  • Justin Campbell (a1)


In this article we give a geometric construction of a tilting perverse sheaf on Drinfeld’s compactification, by applying the nearby cycles functor to a family of nondegenerate Whittaker sheaves. Its restrictions along the defect stratification are shown to be certain perverse sheaves attached to the nilpotent radical of the Langlands dual Lie algebra. We also describe the subquotients of the monodromy filtration using the Picard–Lefschetz oscillators introduced by Schieder. We give an argument that the subquotients are semisimple based on the action, constructed by Feigin, Finkelberg, Kuznetsov, and Mirković, of the Langlands dual Lie algebra on the global intersection cohomology of quasimaps into flag varieties.



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[AG15a] Arinkin, D. and Gaitsgory, D., Singular support of coherent sheaves and the geometric Langlands conjecture , Selecta Math. (N.S.) 21 (2015), 1199.
[AG15b] Arinkin, D. and Gaitsgory, D., Asymptotics of geometric Whittaker coefficients, Preprint (2015),∼gaitsgde/GL/WhitAsympt.pdf.
[Bei87] Beilinson, A., How to glue perverse sheaves , in K-theory, arithmetic, and geometry, Lecture Notes in Mathematics, vol. 1289 (Springer, Berlin, 1987).
[BG02] Braverman, A. and Gaitsgory, D., Geometric Eisenstein series , Invent. Math. 150 (2002), 287384.
[BG08] Braverman, A. and Gaitsgory, D., Deformations of local systems and Eisenstein series , Geom. Funct. Anal. 17 (2008), 17881850.
[Cam16] Campbell, J., A resolution of singularities for Drinfeld’s compactification by stable maps, Preprint (2016), arXiv:1606.01518.
[Cam17] Campbell, J., The big projective module as a nearby cycles sheaf , Selecta Math. (N.S.) 23 (2017), 721726.
[ENV04] Emerton, M., Nadler, D. and Vilonen, K., A geometric Jacquet functor , Duke Math. J. 125 (2004), 267278.
[FFKM99] Feigin, B., Finkelberg, M., Kuznetsov, A. and Mirkovic, I., Semiinfinite flags II , Trans. Amer. Math. Soc. 194 (1999), 113148.
[FGV01] Frenkel, E., Gaitsgory, D. and Vilonen, K., Whittaker patterns in the geometry of moduli spaces of bundles on curves , Ann. of Math. (2) 153 (2001), 699748.
[Gai15] Gaitsgory, D., Outline of the proof of the geometric Langlands conjecture for GL(2) , Astérisque 370 (2015), 1112.
[GR17] Gaitsgory, D. and Rozenblym, N., A study in derived algebraic geometry (American Mathematical Society, Providence, RI, 2017).
[Moc15] Mochizuki, T., Mixed twistor D-modules (Springer, Cham, 2015).
[Ras16] Raskin, S., Chiral principal series categories I: finite-dimensional calculations, Preprint (2016),∼sraskin/cpsi.pdf.
[Sch18] Schieder, S., Picard–Lefschetz oscillators for the Drinfeld–Lafforgue–Vinberg degeneration for SL 2 , Duke Math. J. 167 (2018), 835921.
[Sch17] Schieder, S., Monodromy and Vinberg fusion for the principal degeneration of the space of G-bundles, Preprint (2017), arXiv:1701.01898.
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Nearby cycles of Whittaker sheaves on Drinfeld’s compactification

  • Justin Campbell (a1)


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