Results 171 to 180 of about 676,000 (198)

A note on Galois representations with big image

L'Enseignement mathématique, 2020
Given an integer N ≥ 3, we will first construct reasonably “motivic” representations ρ : Gal(Q/Q(ζN ))→ GL(n,Q`) with open image, for any ` which is 1 mod N and for certain n. We will do this in three different ways.
N. M. Katz
semanticscholar   +1 more source

Lifting and automorphy of reducible mod p Galois representations over global fields

Inventiones Mathematicae, 2020
We prove the modularity of most reducible, odd representations ρ¯:ΓQ→GL2(k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
N. Fakhruddin, Chandrashekhar B. Khare, Stefan Patrikis   +2 more
semanticscholar   +1 more source

ON NONCRITICAL GALOIS REPRESENTATIONS

Journal of the Institute of Mathematics of Jussieu, 2021
AbstractWe propose a conjecture that the Galois representation attached to every Hilbert modular form is noncritical and prove it under certain conditions. Under the same condition we prove Chida, Mok and Park’s conjecture that Fontaine-Mazur L-invariant and Teitelbaum-type L-invariant coincide with each other.
openaire   +2 more sources

Galois Groups, Galois Representations and Iwasawa Theory

Journal of the Indian Institute of Science, 2022
In this article, the author provides a lively picture of the principal questions and the main results in Iwasawa theory. After briefly explaining the role of Leopoldt's conjecture in connection with the number of independent \(\mathbb Z_p\)-extensions of number fields, she introduces Galois representations and mentions the Tate module of elliptic ...
openaire   +1 more source

Arboreal Galois representations

Geometriae Dedicata, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boston, Nigel, Jones, Rafe
openaire   +2 more sources

Moduli spaces of sheaves on K3 surfaces and Galois representations

Selecta Mathematica, 2018
We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the étale cohomology groups (with $${\mathbb {Q}}_\ell ...
Sarah Frei
semanticscholar   +1 more source

Reductions of Galois representations of slope 3 2

Kyoto Journal of Mathematics, 2019
We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{\mathbb{Q}_p}$ of slope $\frac{3}{2}$ and exceptional weights.
Eknath Ghate, Vivek Rai
semanticscholar   +1 more source

A connectedness criterion for ℓ-adic galois representations-adic galois representations

Israel Journal of Mathematics, 1997
To every compatible system of Galois representations of a global fieldK, there is associated a natural invariantK conn, the smallest extension ofK over which the associated algebraic monodromy groups become connected. We present a purely field-theoretic construction ofK conn for all Galois representations arising from ...
Michael Larsen, Richard Pink
openaire   +1 more source

Lifting Galois representations

Inventiones mathematicae, 1999
Let \({\mathbf k}\) be a finite field of characteristic \(p\) and \(G=\text{Gal}(\overline{\mathbb Q}/{\mathbb Q})\). If \(\overline\rho: G\rightarrow \text{GL}_2({\mathbf k})\) is a linear representation one would like to find a noetherian local ring \(A\) of characteristic 0 having \({\mathbf k}\) as a quotient and a continuous representation \(\rho ...
openaire   +1 more source

Icosahedral Galois representations

Pacific Journal of Mathematics, 1997
To the memory of Olga Taussky-Todd ; Mathematics ; Accepted ...
openaire   +2 more sources