Results 31 to 40 of about 590 (49)

UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2017
Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON, DAVIDE REDUZZI, LIANG XIAO   +2 more
doaj   +1 more source

Proof of de Smit's conjecture: a freeness criterion

, 2017
Let $A\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper "The ...
Brochard, Sylvain
core   +1 more source

Lifting G-Valued Galois Representations when $\ell \neq p$

Forum of Mathematics, Sigma
In this paper, we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$ .
Jeremy Booher, Sean Cotner, Shiang Tang
doaj   +1 more source

COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES

Forum of Mathematics, Sigma, 2016
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj   +1 more source

A characterization of ordinary modular eigenforms with CM [PDF]

, 2013
For a rational prime $p \geq 3$ we show that a $p$-ordinary modular eigenform $f$ of weight $k\geq 2$, with $p$-adic Galois representation $\rho_f$, mod ${p^m}$ reductions $\rho_{f,m}$, and with complex multiplication (CM), is characterized by the ...
Adibhatla, Rajender, Tsaknias, Panagiotis   +1 more
core   +1 more source

Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4

, 2018
We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve ...
Kiming, Ian, Rustom, Nadim
core   +1 more source

Local-global compatibility for regular algebraic cuspidal automorphic representations when $\ell \neq p$

Forum of Mathematics, Sigma
We prove the compatibility of local and global Langlands correspondences for $\operatorname {GL}_n$ up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne [10] and Scholze [18]. More precisely, let $r_p(
Ila Varma
doaj   +1 more source

Root numbers of elliptic curves in residue characteristic 2

, 2006
To determine the global root number of an elliptic curve defined over a number field, one needs to understand all the local root numbers. These have been classified except at places above 2, and in this paper we attempt to complete the classification. At
Dokchitser, T., Dokchitser, V.
core   +2 more sources

Modularity of trianguline Galois representations

Forum of Mathematics, Sigma
We use the theory of trianguline $(\varphi ,\Gamma )$ -modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients.
Rebecca Bellovin
doaj   +1 more source

An irreducibility criterion for group representations, with arithmetic applications

, 2010
We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R.
Longo, M., Vigni, S.
core   +2 more sources