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...

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...

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

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...

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

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

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

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

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...

theory to define important subcategories of p-adic Galois representations of the absolute Galois group of local and global fields. Let G be a group and...

to semisimple representation theory questions about a quiver. Galois representation Glossary of representation theory Group representation Itô's theorem...

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...

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...

81, 1985, p. 515). He introduced the concept of geometric Galois representation of the Galois group of a number field. He also worked on Bloch-Kato conjectures...

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

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...

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

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}...

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,...

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

integer combination. The reasons are studied in depth in Galois module theory. The regular representation of a group ring is such that the left-hand and right-hand...

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...

Galois rings are a type of finite commutative rings which generalize both the finite fields and the rings of integers modulo a prime power. A Galois ring...

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

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...

mathematics, a deformation ring is a ring that controls liftings of a representation of a Galois group from a finite field to a local field. In particular for...

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...

equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory...

Langlands (1967, 1970). It seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local...