An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(n,Z)

Details An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(n,Z) An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(n,Z)

1999-06-07

arxiv.org/abs/math/9906216v1

Mathematics

Number Theory

Scientific paper

The conjecture of Serre referred in the title is the one about modularity of odd Galois representations into GL(2,F) where F is a finite field of characteristic p. We present an analogous conjecture where GL(2) is replaced by GL(n). We explain the analogue of "oddness." We then present some theoretical and experimental evidence for the conjecture, primarily when n = 3. Our conjecture does not require the Galois representation to be irreducible. Our most interesting examples involve the sum of an irreducible even 2-dimensional representation and a 1-dimensional representation.

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