Abstract
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= GL n.
| Original language | English (US) |
|---|---|
| Article number | 13 |
| Journal | Selecta Mathematica, New Series |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2022 |
Bibliographical note
Funding Information:The paper is inspired by the lectures given by Ginzburg and Ngô on their works [, ]. I thank Roman Bezrukavnikov, Tanmay Deshpande, Victor Ginzburg, Sam Gunningham, Augustus Lonergan, David Nadler, Ngô Bao Châu, Lue Pan, and Zhiwei Yun for useful discussions. I thank the anonymous referee for valuable comments. I am grateful for the support of NSF grant DMS-1702337 and DMS-2001257, and the S. S. Chern Foundation.
Publisher Copyright:
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