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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: doud@math.byu.edu

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Three-dimensional Galois representations with conjectural connections to arithmetic cohomology

in Number Theory for the Millennium, A.K. Peters, Boston, 2002, pp. 365-375.

Abstract We give an example of a special case of a conjecture relating Galois representations and arithmetic cohomology. The Galois representation is among the first irreducible representations known which is not a twis of a symmetric square of a two-dimensional representation, but is apparently related to a cohomology class. The conjecture predicts the existence of several "companion forms," and we give computationon evidence that these forms exist.

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