mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used...

arithmetic dynamics, an arboreal Galois representation is a continuous group homomorphism between the absolute Galois group of a field and the automorphism...

In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated...

about Galois representations of elliptic curves. He then uses this result to prove that all semistable curves are modular, by proving that the Galois representations...

Asymptotic representation theory, Lecture notes 2009–2010 https://ncatlab.org/nlab/show/asymptotic+representation+theory Galois representation Glossary...

true. In mathematical terms, Ribet's theorem shows that if the Galois representation associated with an elliptic curve has certain properties, then that...

encryption, and uses arithmetic in the Galois field GF(2128) to compute the authentication tag; hence the name. Galois Message Authentication Code (GMAC)...

Galois deformation Galois descent Galois extension Galois field Galois geometry Galois group Absolute Galois group Galois LFSRs Galois module Galois representation...

Serre (1975, 1987), states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form. A stronger version...

{SL} _{2}(\mathbb {R} )} . Every modular form is attached to a Galois representation. The term "modular form", as a systematic description, is usually...

cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the...

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...

L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced in 1923 by Emil Artin...

relate the structure of Galois groups in algebraic number theory to automorphic forms and, more generally, the representation theory of algebraic groups...

a p {\displaystyle p} -adic representation of K {\displaystyle K} (or of G K {\displaystyle G_{K}} , the absolute Galois group of K {\displaystyle K}...

over Zp with a linear action of the absolute Galois group GK of K. Thus, it is a Galois representation also referred to as the p-adic cyclotomic character...

mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...

groups Mumford–Tate group and motivic Galois group arise from categories of Hodge structures, category of Galois representations and motives through Tannakian...

of an Artin L-function. Suppose that L is a finite Galois extension of the local field K, with Galois group G. If χ {\displaystyle \chi } is a character...

of deformation theory is with Galois deformations. It allows us to answer the question: If we have a Galois representation G → GL n ⁡ ( F p ) {\displaystyle...

integral ideal, which is analogous to the Artin conductor of a Galois representation. It is given as a product of prime ideals, together with associated...

question of the Galois representation on the Tate module of an abelian variety A. Conjecturally, the image of such a Galois representation, which is an l-adic...

are central to differential Galois theory, a variant of Galois theory dealing with linear differential equations. Galois theory studies algebraic extensions...

GF(pn) and is also called the Galois field of order pn, in honor of the founder of finite field theory, Évariste Galois. GF(p), where p is a prime number...

good reduction, in a definite sense, at all primes p for which the Galois representation ρ on the étale cohomology groups of V is unramified. For those,...

Évariste Galois in the 1830s, who introduced the term group (French: groupe) for the symmetry group of the roots of an equation, now called a Galois group...

constructs automorphic forms and their correspondent functions as embeddings of Galois groups to their underlying global field extensions. In this formulation...

p^{-1}(xg)} is a well-defined linear map. Galois Galois representation. good A good filtration of a representation of a reductive group G is a filtration...

1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He...

group on a set of size n is the Galois group of the general polynomial of degree n and plays an important role in Galois theory. In invariant theory, the...