Results 51 to 60 of about 5,376,358 (214)

Introduction to Galois Theory

Formalized Mathematics
Summary This article continues a series devoted to the formalization of the Fundamental Theorem of Galois Theory using the Mizar proof assistant. We define groups of automorphisms and fixed fields and establish their fundamental properties.
Christoph Schwarzweller, Agnieszka Rowinska-Schwarzweller   +1 more
openaire   +2 more sources

On the integral simplicial volume of cyclic covers of mapping tori

Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.
Abstract In this paper, we investigate the asymptotic behavior of the integral simplicial volume of cyclic covers of manifolds that fiber over the circle with fiber given by an n$n$‐dimensional torus. By studying the integral filling volume—an invariant introduced by Frigerio and the first author—for the monodromy, we establish both lower and upper ...
Federica Bertolotti, Ervin Hadžiosmanović   +1 more
wiley   +1 more source

Construction of q-ary(n,M,d)-codes in PG(2,16)

Wasit Journal for Pure Sciences, 2023
The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective q-ary (n, M, d) -code such that the parameters length of code n, the maximum value size code M, and the minimum ...
Dunya Fareeq Fendi, Nada Yassen Kasm Yahya   +1 more
doaj   +1 more source

Localic Galois theory

Advances in Mathematics, 2003
In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its galois group. We first state and prove the (dual) categorical interpretation of of this statement, which is a theorem ...
openaire   +3 more sources

Inducing Coverings on Hilbert Schemes

Mathematische Nachrichten, Volume 299, Issue 8, Page 2177-2190, August 2026.
ABSTRACT We find an explicit geometric description of all coverings of Hilb2(Σ)$\operatorname{Hilb}^{2}(\Sigma)$ when Σ$\Sigma$ is a normal, complex, quasi‐projective surface with finite fundamental group. We then apply this construction to show that if Σ$\Sigma$ is an irreducible symplectic surface then Hilb2(Σ)$\operatorname{Hilb}^{2}(\Sigma)$ is an ...
Lucas Li Bassi, Filippo Papallo
wiley   +1 more source

A trace–path integral formula over function fields

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We show that an arithmetic path integral over the ℓ$\ell$‐torsion of a Jacobian J[ℓ]$J[\ell]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ])$H(J[\ell])$, up to an explicitly determined sign.
Yan Yau Cheng
wiley   +1 more source

Classical Galois theory [PDF]

, 1972
The purpose of this thesis is to examine the correspondence between groups of automorphsims and fields and to prove the Fundamental Theorem of Galois Theory. The fields under consideration are infinite.
Mastin, Millicent Gay, NC DOCKS at The University of North Carolina at Greensboro   +1 more
core  

Quantum Information: A Brief Overview and Some Mathematical Aspects

Mathematics, 2018
The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally
Maurice R. Kibler
doaj   +1 more source

On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley   +1 more source

Real difference Galois theory

, 2017
International audienceIn this paper, we develop a difference Galois theory in the setting of real fields. After proving the existence and uniqueness of the real Picard-Vessiot extension, we define the real difference Galois group and prove a Galois ...
Thomas Dreyfus, Dreyfus, Thomas
core   +1 more source