Journal
SELECTA MATHEMATICA-NEW SERIES
Volume 21, Issue 1, Pages 1-199Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00029-014-0167-5
Keywords
Cohomological support; Geometric Langlands program; Derived algebraic geometry; Arthur parameters
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Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1452276] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1063470] Funding Source: National Science Foundation
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We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Artin stack, where quasi-smooth means that it is a locally complete intersection in the derived sense. This develops the idea of cohomological support of coherent sheaves on a locally complete intersection scheme introduced by D. Benson, S. B. Iyengar, and H. Krause. We study the behavior of singular support under the direct and inverse image functors for coherent sheaves. We use the theory of singular support of coherent sheaves to formulate the categorical geometric Langlands conjecture. We verify that it passes natural consistency tests: It is compatible with the geometric Satake equivalence and with the Eisenstein series functors. The latter compatibility is particularly important, as it fails in the original naive form of the conjecture.
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