Results 21 to 30 of about 432 (61)

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

Forum of Mathematics, Sigma, 2014
We extend the modularity lifting result of P. Kassaei (‘Modularity lifting in parallel weight one’,J. Amer. Math. Soc. 26 (1) (2013), 199–225) to allow Galois representations with some ramification at
PAYMAN L. KASSAEI, SHU SASAKI, YICHAO TIAN   +2 more
doaj   +1 more source

Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$

Forum of Mathematics, Sigma, 2014
We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ .
JACK A. THORNE
doaj   +1 more source

Extensions of abelian varieties defined over a number field [PDF]

, 2003
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.Comment: 11 ...
Bosch, Conrad, Cremona, Diamond, Diamond, Faltings, Flach, Flach, Hida, Hida, Masser, Matthew A. Papanikolas, Mazur, Milne, Milne, Milne, Milne, Niranjan Ramachandran, Papanikolas, Reverter, Serre, Tate, Ullmo, Zagier   +23 more
core   +4 more sources

Heegner points and p-adic L-functions for elliptic curves over certain totally real fields

, 2011
For an elliptic curve E over Q satisfying suitable hypotheses, Bertolini and Darmon have derived a formula for the Heegner point on E in terms of the central derivative of the two variable p-adicL-function associated toE.
Chung Pang Mok
semanticscholar   +1 more source

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

Interpolating coefficient systems and $p$-ordinary cohomology of arithmetic groups

, 2011
We present an approach to Hida’s theory of p-adically interpolating the ordinary cohomology of arithmetic groups and we discuss some application of this approach to special values of L-functions. Mathematics Subject Classification (2010).
G. Harder
semanticscholar   +1 more source

Ordinary Modular Forms and Companion Points on the Eigencurve [PDF]

, 2013
We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f.Comment: 12 ...
Bergdall, John
core   +4 more sources

Congruences for traces of singular moduli

, 2004
We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.Comment: 8 pages, to appear in The Ramanujan ...
Osburn, Robert
core   +1 more source

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

A level raising result for modular Galois representations modulo prime powers [PDF]

, 2012
In this work we provide a level raising theorem for $\mod \lambda^n$ modular Galois representations. It allows one to see such a Galois representation that is modular of level $N$, weight 2 and trivial Nebentypus as one that is modular of level $Np$, for
Tsaknias, Panagiotis
core   +1 more source