Spectral action in Betti Geometric Langlands
| Autor: | Zhiwei Yun, David Nadler |
|---|---|
| Přispěvatelé: | Massachusetts Institute of Technology. Department of Mathematics |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Structure (category theory) 0102 computer and information sciences Reductive group 01 natural sciences Action (physics) Moduli 14D24 22E57 Mathematics - Algebraic Geometry Nilpotent Mathematics::Algebraic Geometry 010201 computation theory & mathematics FOS: Mathematics Sheaf Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Indecomposable module Constant (mathematics) Algebraic Geometry (math.AG) Mathematics - Representation Theory Mathematics |
| Zdroj: | arXiv |
| ISSN: | 1565-8511 0021-2172 |
| DOI: | 10.1007/s11856-019-1871-9 |
| Popis: | Let $X$ be a smooth projective curve, $G$ a reductive group, and $Bun_G(X)$ the moduli of $G$-bundles on $X$. For each point of $X$, the Satake category acts by Hecke modifications on sheaves on $Bun_G(X)$. We show that, for sheaves with nilpotent singular support, the action is locally constant with respect to the point of $X$. This equips sheaves with nilpotent singular support with a module structure over perfect complexes on the Betti moduli $Loc_{G^\vee}(X)$ of dual group local systems. In particular, we establish the "automorphic to Galois" direction in the Betti Geometric Langlands correspondence -- to each indecomposable automorphic sheaf, we attach a dual group local system -- and define the Betti version of V. Lafforgue's excursion operators. Comment: 30 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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