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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The category of singularities as a crystal and global Springer fibers
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by D. Arinkin and D. Gaitsgory HTML | PDF
J. Amer. Math. Soc. 31 (2018), 135-214 Request permission

Abstract:

We prove the “gluing conjecture” on the spectral side of the categorical geometric Langlands conjecture. The key tool is the structure of crystal on the category of singularities, which allows one to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
References
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Additional Information
  • D. Arinkin
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: arinkin@math.wisc.edu
  • D. Gaitsgory
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
  • Email: gaitsgde@math.harvard.edu
  • Received by editor(s): May 13, 2015
  • Received by editor(s) in revised form: January 18, 2017
  • Published electronically: May 8, 2017
  • Additional Notes: The research of the first author is partially supported by NSF grant DMS-1101558.
    The research of the second author is partially supported by NSF grant DMS-1063470.
  • © Copyright 2017 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 31 (2018), 135-214
  • MSC (2010): Primary 14F05, 14H60
  • DOI: https://doi.org/10.1090/jams/882
  • MathSciNet review: 3718453