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Darrin Doud

214 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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Cited by

• Florian Herzig, The weight in a Serre-type conjecture for tame n-dimensional Galois representations, Harvard University Ph.D. Thesis, 2006.
• Florian Herzig, The weight in a Serre-type conjecture for tame n-dimensional Galois representations, Duke Math. J., 149 (2009), 37--116.
• Andrzej Dąbrowski, Hipoteza Serre'a o modularności i nowe dowody Wieldiego Twierdzenia Fermata, Wiad. Mat. 45 (2009), 3-24.
• Matthew Emerton, Toby Gee, and Florian Herzig, Weight cycling and Serre-type conjectures for unitary groups, Duke Math. J. 162 (2013), 1649-1722.
• Toby Gee, Florian Herzig, and David Savitt, General Serre Weight Conjectures, J. Eur. Math. Soc., 20 (2018), 2859-2949.