A vanishing conjecture: the GLn case

• Tsao-Hsien Chen ^[1]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
• Idioma: inglés
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• Resumen

  • In this article we propose a vanishing conjecture for a certain class of ℓ-adic complexes on a reductive group G which can be regarded as a generalization of the acyclicity of the Artin–Schreier sheaf. We show that the vanishing conjecture contains, as a special case, a conjecture of Braverman and Kazhdan on the acyclicity of ρ-Bessel sheaves (Braverman and Kazhdan in Geom Funct Anal I:237–278, 2002). Along the way, we introduce a certain class of Weyl group equivariant ℓ-adic complexes on a maximal torus called central complexes and relate the category of central complexes to the Whittaker category on G. We prove the vanishing conjecture in the case when G=GLn.