## The category of singularities as a crystal and global Springer fibers

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D. Arinkin and D. Gaitsgory
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**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