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Darrin Doud

314 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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Supersingular Galois representations and a generalization of a conjecture of Serre

Experimental Mathematics. 16:1 (2007), 119-128.

Abstract Serre's conjecture relates two-dimensional odd irreducible characteristic p Galois representations to modular forms. We discuss a generalization of this conjecture to higher-dimensional Galois representations. In particular, for n-dimensional Galois representations which are irreducible when restricted to the decomposition group at p, we strengthen a conjecture of Ash, Doud, and Pollack. We then give computational evidence for this conjecture in the case of three-dimensional representations.

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