The weight in a Serre-type conjecture for tame n-dimensional Galois representations

Details The weight in a Serre-type conjecture for tame n-dimensional Galois representations The weight in a Serre-type conjecture for tame n-dimensional Galois representations

2008-03-03

arxiv.org/abs/0803.0185v2

Duke Mathematical Journal 149 (2009), no. 1, 37-116

Mathematics

Number Theory

68 pages, revised (mainly added appendix that generalises Jantzen's theorem on the reduction modulo p of Deligne--Lusztig repr

Scientific paper

10.1215/00127094-2009-036

We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the previous conjecture of Ash, Doud, Pollack, and Sinnott. Computational evidence for these extra weights is provided by calculations of Doud and Pollack. We obtain theoretical evidence for n = 4 using automorphic inductions of Hecke characters.

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