Modular Forms for GL(3) and Galois Representations
نویسندگان
چکیده
A description and an example are given of numerical experiments which look for a relation between modular forms for certain congruence subgroups of SL(3, ZZ) and Galois representations.
منابع مشابه
Modular Forms for GL ( 3 ) and
A description and an example are given of numerical experiments which look for a relation between modular forms for certain congruence subgroups of SL(3; Z Z) and Galois representations.
متن کاملCrystalline Representations for GL(2) over Quadratic Imaginary Fields
Let K be a quadratic imaginary field and π an irreducible regular algebraic cuspidal automorphic representation of GL(2,AK). Under the assumption that the central character χπ is isomorphic to its complex conjugate, Taylor et al. associated p-adic Galois representations ρπ,p : GK → GL(2,Qp) which are unramified except at finitely many places, and such that the truncated L-function of the Galois...
متن کاملp-ADIC FAMILIES AND GALOIS REPRESENTATIONS FOR GSp(4) AND GL(2)
In this brief article we prove local-global compatibility for holomorphic Siegel modular forms with Iwahori level. In previous work we proved a weaker version of this result (up to a quadratic twist) and one of the goals of this article is to remove this quadratic twist by different methods, using p-adic families. We further study the local Galois representation at p for nonregular holomorphic ...
متن کاملOn Symmetric Power L-invariants of Iwahori Level Hilbert Modular Forms
We compute the arithmetic L-invariants (of Greenberg–Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of symmetric powers and the study of analytic Galois representations on p-adic families of automorphic forms over symplectic and unitary groups. Combining thes...
متن کاملCompatible Systems of `-adic Representations of Dimension Two
where E`n denotes the group of `-torsion points of E. The Galois group GK = Gal(K̄/K) acts continuously on T` and therefore on V`. In a series of works ([5], [6], [8], [9]), Serre investigated the image, Γ`, of GK in GL(V`). If E has complex multiplication over C, Γ` is contained in a Cartan subgroup of GL(V`) (resp. the normalizer of a Cartan) if K contains (resp. does not contain) the endomorp...
متن کامل