Results 61 to 70 of about 2,228 (208)

Moments of the Dedekind zeta function [PDF]

, 2013
We study analytic aspects of the Dedekind zeta function of a Galois extension. Specifically, we are interested in its mean values. In the first part of this thesis we give a formula for the second moment of the Dedekind zeta function of a quadratic ...
Heap, Winston
core  

THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS

Forum of Mathematics, Pi, 2014
We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate representations of the absolute Galois group $G_{K}$, $K$ a finite extension of $\mathbb{Q}_{p}$, for any $p>2$ (up to the question of determining precise ...
TOBY GEE, MARK KISIN
doaj   +1 more source

Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations [PDF]

, 2017
peer reviewedThis article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem.
Dieulefait, Luis Víctor, ARIAS DE REYNA DOMINGUEZ, Sara, Dieulefait, Luis, WIESE, Gabor   +3 more
core   +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

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

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

A history of Galois fields

Khronos, 2016
This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
doaj  

On local Galois deformation rings: generalised reductive groups

Forum of Mathematics, Pi
We study deformation theory of mod p Galois representations of p-adic fields with values in generalised reductive group schemes, such as L-groups and C-groups.
Vytautas Paškūnas, Julian Quast
doaj   +1 more source

On Galois representations of weight one

Documenta Mathematica, 2014
A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p
openaire   +4 more sources

Locally indecomposable Galois representations [PDF]

, 2011
In a previous paper the authors showed that, under some technical conditions, the local Galois representations attached to the members of a non-CM family of ordinary cusp forms are indecomposable for all except possibly finitely many members of the ...
Ghate, Eknath, Eknath Ghate, Vatsal, Vinayak, Vinayak Vatsal   +3 more
core   +1 more source