Browsing by Subject "Galois theory"
Now showing items 114 of 14

Computing congruences of modular forms and Galois representations modulo prime powers
(2010)
Article
Open AccessThis article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime ... 
Congruences between modular forms and lowering the level mod l^n
(2009)
Article
Open AccessIn this article we study the behavior of inertia groups for modular Galois mod ℓn representations and in some cases we give a generalization of Ribet’s lowering the level result. 
Differential galois theory and nonintegrability of planar polynomial vector fields
(20180226)
Article
Restricted access  publisher's policyWe study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular ... 
Equations of hyperelliptic Shimura curves
(2012)
Article
Open AccessWe describe a method for computing equations of hyperelliptic Shimura curves attached to indefinite quaternion algebras over Q and Atkin–Lehner quotients of them. It exploits Cerednik–Drinfeld 's nonarchimedean uniformization ... 
From Galois to Hopf Galois: theory and practice
(201509)
Article
Open AccessHopf Galois theory expands the classical Galois theory by con sidering the Galois property in terms of the action of the group algebra k [ G ] on K/k and then replacing it by the action of a Hopf algebra. We review the ... 
Generic Galois extensions for SL_2(F_5) over Q
(Mathematical Publishing, 2007)
Article
Open AccessLet $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n1}$ be the corresponding double cover of $A_{n1}$ or $S_{n1}$. For every odd $n\geq 3$ and every field $k$ of ... 
Induced Hopf Galois structures
(20160701)
Article
Open AccessFor a ¿nite Galois extension K/k and an intermediate ¿eld F such that Gal(K/F)has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois ... 
Nonisomorphic Hopf Galois structures with isomorphic underlying Hopf algebras
(20141030)
Article
Restricted access  publisher's policyWe give a degree 8 nonnormal separable extension having two nonisomorphic Hopf Galois structures with isomorphic underlying Hopf algebras. 
On fields of definition of torsion points of elliptic curves with complex multiplication
(201106)
Article
Open AccessFor any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ... 
On the integrability of polynomial fields in the plane by means of PicardVessiot theory
(20120112)
External research report
Open AccessWe study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ... 
Ordinary CM forms and local Galois representations
(Universitat Politècnica de Catalunya, 200907)
Master thesis
Open Access"The padic Galois representation \rho_f attached to a pordinary newform f of weight k>1 is known to be reducible when restricted to a decomposition group D_p at p. Ralph Greenberg asked for a characterization of those f ... 
ScholzReichardt’s Theorem
(Universitat Politècnica de Catalunya, 201807)
Bachelor thesis
Open AccessIn this thesis we examine the proof of a theorem due to Scholz and Reichardt in 1937. It states that any odd pgroup occurs as a Galois group over the rationals. 
The Hopf Galois property in subfield lattices
(20160101)
Article
Open AccessLet K/k be a finite separable extension, n its degree and (K) over tilde /k its Galois closure. For n <= 5, Greither and Pareigis show that all Hopf Galois extensions are either Galois or almost classically Galois and they ... 
The KroneckerWeber Theorem
(Universitat Politècnica de Catalunya, 201807)
Bachelor thesis
Open AccessIn this bachelor's thesis we give a complete proof of the KroneckerWeber theorem, which states that every finite abelian extension over the field of rational numbers Q is contained in some cyclotomic extension of Q. We ...