Results 21 to 30 of about 590 (49)

EULER SYSTEMS FOR HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2018
We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces.
ANTONIO LEI, DAVID LOEFFLER, SARAH LIVIA ZERBES   +2 more
doaj   +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

On local Galois deformation rings: generalised tori

Forum of Mathematics, Sigma
We study deformation theory of mod p Galois representations of p-adic fields with values in generalised tori, such as L-groups of (possibly non-split) tori.
Vytautas Paškūnas, Julian Quast
doaj   +1 more source

Components of moduli stacks of two-dimensional Galois representations

Forum of Mathematics, Sigma
In the article [CEGS20b], we introduced various moduli stacks of two-dimensional tamely potentially Barsotti–Tate representations of the absolute Galois group of a p-adic local field, as well as related moduli stacks of Breuil–Kisin modules with descent ...
Ana Caraiani, Matthew Emerton, Toby Gee, David Savitt   +3 more
doaj   +1 more source

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

COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$

Forum of Mathematics, Sigma, 2019
We construct, over any CM field, compatible systems of $l$-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all $l$) algebraic monodromy groups equal to the exceptional group of type $E_{6}$.
GEORGE BOXER, FRANK CALEGARI, MATTHEW EMERTON, BRANDON LEVIN, KEERTHI MADAPUSI PERA, STEFAN PATRIKIS   +5 more
doaj   +1 more source

Smith theory and cyclic base change functoriality

Forum of Mathematics, Pi
Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields.
Tony Feng
doaj   +1 more source

SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS

Forum of Mathematics, Sigma, 2016
A generalization of Serre’s Conjecture asserts that if $F$ is a totally real field, then certain characteristic
LASSINA DEMBÉLÉ, FRED DIAMOND, DAVID P. ROBERTS   +2 more
doaj   +1 more source

The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms

Forum of Mathematics, Pi
We prove the Ramanujan and Sato–Tate conjectures for Bianchi modular forms of weight at least $2$ . More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\operatorname {\mathrm {GL}}_2 ...
George Boxer, Frank Calegari, Toby Gee, James Newton, Jack A. Thorne   +4 more
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