Now showing items 1-14 of 14

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

    Taixes Ventosa, Xavier; Wiese, Gabor (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 

    Dieulefait, Luis Victor; Taixes Ventosa, Xavier (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 

    Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (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 

    Molina Blanco, Santiago (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 

    Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Maria Montserrat (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 

    Plans Berenguer, Bernat (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 ...
  • On elliptic Galois representations and genus-zero modular units 

    Fernández González, Julio; Lario Loyo, Joan Carles (2006-07-03)
    Article
    Open Access
    Given an odd prime \,$p$\, and a representation $\varrho$\, of the absolute Galois group of a number field $k$ onto $\mathrm{PGL}_2(\mathbb{F}_p)$ with cyclotomic determinant, the moduli space of elliptic curves defined ...
  • On fields of definition of torsion points of elliptic curves with complex multiplication 

    Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (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 

    Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (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 

    Castellà Cabello, Francesc (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 ...
  • Polynomials in finite geometry 

    Ball, Simeon Michael; Blokhuis, Aart (Università degli studi di Napoli. Dipartimento di Matematica, 1999-11-01)
    Part of book or chapter of book
    Open Access
  • Rational points on twists of X0(63) 

    Bruin, Nils; Fernández González, Julio; González i Rovira, Josep; Lario Loyo, Joan Carles (2006-02-07)
    Article
    Open Access
    Let $\varrho\colon G_\mathbb{Q}\longrightarrow PGL_2(\mathbb{F}_p)$ be a Galois representation with cyclotomic determinant, and let $N>1$ be an integer that is square mod $p$. There exist two twisted modular curves ...
  • The Hopf Galois property in subfield lattices 

    Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Maria Montserrat (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 polynomial method in Galois geometries 

    Ball, Simeon Michael (Nova Science Publishers, 2012)
    Part of book or chapter of book
    Restricted access - publisher's policy
    The polynomial method refers to the application of polynomials to combinatorial problems. The method is particularly effective for Galois geometries and a number of problems and conjectures have been solved using the ...