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1	Totally Real Galois Representations in Characteristic 2 and Arithmetic Cohomology de Melo, Heather Aurora Florence 02 November 2005 (has links) (PDF) The purpose of this paper is to provide new examples supporting a conjecture of Ash, Doud, and Pollack. This conjecture involves Galois representations taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant. Serre conjecture Galois representations Ash Doud Pollack computation Mathematics
2	Explicit Computations Supporting a Generalization of Serre's Conjecture Hansen, Brian Francis 03 June 2005 (has links) (PDF) Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation. Serre conjecture Galois representations modular forms complex approximation Ash Doud Pollack computation Mathematics