Conjecture de type de Serre et formes compagnons pour GSp4
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Abstract
We present a Serre-type conjecture on the modularity of four-dimensional symplectic mod 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.
©[2013] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Conjecture de type de Serre et formes compagnons pour GSp4
- Extension of plurisubharmonic functions with growth control
- Additivity and non-additivity for perverse signatures
- MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
- The prime geodesic theorem
- Inequities in the Shanks–Rényi prime number race: An asymptotic formula for the densities
- Klein approximation and Hilbertian fields
- Ricci flow on asymptotically conical surfaces with nontrivial topology
Articles in the same Issue
- Conjecture de type de Serre et formes compagnons pour GSp4
- Extension of plurisubharmonic functions with growth control
- Additivity and non-additivity for perverse signatures
- MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
- The prime geodesic theorem
- Inequities in the Shanks–Rényi prime number race: An asymptotic formula for the densities
- Klein approximation and Hilbertian fields
- Ricci flow on asymptotically conical surfaces with nontrivial topology
