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The category of singularities as a crystal and global Springer fibers


Authors: D. Arinkin and D. Gaitsgory
Journal: J. Amer. Math. Soc.
MSC (2010): Primary 14F05, 14H60
DOI: https://doi.org/10.1090/jams/882
Published electronically: May 8, 2017
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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.


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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

DOI: https://doi.org/10.1090/jams/882
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.
Article copyright: © Copyright 2017 American Mathematical Society