## The Buzzard–Diamond–Jarvis conjecture for unitary groups

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- by Toby Gee, Tong Liu and David Savitt PDF
- J. Amer. Math. Soc.
**27**(2014), 389-435 Request permission

## Abstract:

Let $p>2$ be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod $p$ representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of $(\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.## References

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## Additional Information

**Toby Gee**- Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom
- Email: toby.gee@imperial.ac.uk
**Tong Liu**- Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
- MR Author ID: 638721
- Email: tongliu@math.purdue.edu
**David Savitt**- Affiliation: Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721-0089
- Email: savitt@math.arizona.edu
- Received by editor(s): July 5, 2012
- Received by editor(s) in revised form: May 15, 2013
- Published electronically: July 3, 2013
- Additional Notes: The second author was partially supported by NSF grant DMS-0901360.

The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032. - © Copyright 2013 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**27**(2014), 389-435 - MSC (2010): Primary 11F33, 11F80
- DOI: https://doi.org/10.1090/S0894-0347-2013-00775-4
- MathSciNet review: 3164985