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- Title
Conjecture de type de Serre et formes compagnons pour <sub>4</sub>.
- Authors
Herzig, Florian; Tilouine, Jacques
- Abstract
We present a Serre-type conjecture on the modularity of four-dimensional symplectic p Galois representations. We assume that the Galois representation is irreducible and odd (in the symplectic sense). The modularity condition is formulated using the étale and the algebraic de Rham cohomology of Siegel modular varieties of level prime to p. We concentrate on the case when the Galois representation is ordinary at p and we give a corresponding list of Serre weights. When the representation is moreover tamely ramified at p, we conjecture that all weights of this list are modular, otherwise we describe a subset of weights on the list that should be modular. We propose a construction of de Rham cohomology classes using the dual BGG complex, which should realise some of these weights.
- Subjects
NUMBER theory; GALOIS cohomology; SIEGEL domains; GALOIS theory; COHOMOLOGY theory
- Publication
Journal für die Reine und Angewandte Mathematik, 2013, Vol 2013, Issue 676, p1
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/CRELLE.2011.190