Now showing items 1-14 of 14

• Computing congruences of modular forms and Galois representations modulo prime powers ﻿

(2010)
Article
Open Access
This 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 Access
In 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 non-integrability of planar polynomial vector fields ﻿

(2018-02-26)
Article
Restricted access - publisher's policy
We 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 Access
We 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 non-archimedean uniformization ...
• From Galois to Hopf Galois: theory and practice ﻿

(2015-09)
Article
Open Access
Hopf 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 Access
Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of ...
• Induced Hopf Galois structures ﻿

(2016-07-01)
Article
Open Access
For 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 ...
• Non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras ﻿

(2014-10-30)
Article
Restricted access - publisher's policy
We give a degree 8 non-normal separable extension having two non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras.
• On fields of definition of torsion points of elliptic curves with complex multiplication ﻿

(2011-06)
Article
Open Access
For 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 Picard-Vessiot theory ﻿

(2012-01-12)
External research report
Open Access
We 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, 2009-07)
Master thesis
Open Access
"The p-adic Galois representation \rho_f attached to a p-ordinary 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 ...
• Scholz-Reichardt’s Theorem ﻿

(Universitat Politècnica de Catalunya, 2018-07)
Bachelor thesis
Open Access
In this thesis we examine the proof of a theorem due to Scholz and Reichardt in 1937. It states that any odd p-group occurs as a Galois group over the rationals.
• The Hopf Galois property in subfield lattices ﻿

(2016-01-01)
Article
Open Access
Let 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 Kronecker-Weber Theorem ﻿

(Universitat Politècnica de Catalunya, 2018-07)
Bachelor thesis
Open Access
In this bachelor's thesis we give a complete proof of the Kronecker-Weber theorem, which states that every finite abelian extension over the field of rational numbers Q is contained in some cyclotomic extension of Q. We ...