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International Mathematics Research Notices Advance Access originally published online on March 2, 2009
International Mathematics Research Notices (2009) 2009:2303-2317, doi:10.1093/imrn/rnp017 published on June 16, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Explicit Reduction Modulo p of Certain Two-Dimensional Crystalline Representations

Kevin Buzzard1 and Toby Gee2

1 Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ, UK
2 Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, MA 02138, USA

Correspondence: Correspondence to be sent to: tobygee{at}gmail.com

In this paper, we use the p-adic local Langlands correspondence for Formula to explicitly compute the reduction modulo p of certain two-dimensional crystalline representations of small slope, and give applications to modular forms.


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