Now showing items 1-8 of 8

  • Abelian varieties with many endomorphisms and their absolutely simple factors 

    Guitart Morales, Xavier (2012)
    Article
    Restricted access - publisher's policy
    We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties ...
  • Computation of ATR Darmon points on nongeometrically modular elliptic curves 

    Guitart Morales, Xavier; Masdeu, Marc (2013-03)
    Article
    Restricted access - publisher's policy
    ATR points were introduced by Darmon as a conjectural con- struction of algebraic points on certain elliptic curves for which the Heegner-point method is not in general available. So far, the only numerical evidence, ...
  • Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field 

    Fite Naya, Francesc; Guitart Morales, Xavier (2018-07-01)
    Article
    Open Access
    Let A/Q be an abelian variety of dimension g = 1 that is isogenous over Q to Eg, where E is an elliptic curve. If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition ...
  • Modular abelian varieties over number fields 

    Guitart Morales, Xavier; Quer Bosor, Jordi (2014)
    Article
    Restricted access - publisher's policy
    The main result of this paper is a characterization of the abelian varieties B=K defined over Galois number fields with the property that the L-function L(B=K; s) is a product of L-functions of non-CM newforms over Q for ...
  • On the modularity level of modular abelian varieties over number fields 

    Gonzalez Jimenez, Enrique; Guitart Morales, Xavier (2010-07)
    Article
    Open Access
    Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety A f over certain number fields L. The strategy we follow ...
  • On the rank and the convergence rate toward the Sato-Tate measure 

    Fite Naya, Francesc; Guitart Morales, Xavier (2019-07-13)
    Article
    Open Access
    Let A be an abelian variety defined over a number field and let G denote its Sato–Tate group. Under the assumption of certain standard conjectures on L -functions attached to the irreducible representations of G, we study ...
  • Parametrization of Abelian K-surfaces with quaternionic multiplication 

    Guitart Morales, Xavier; Molina Blanco, Santiago (Elsevier, 2009-12)
    Article
    Restricted access - publisher's policy
    We prove that the Abelian K-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the quotient of certain Shimura curves by the group of their ...
  • Tipus de reduccions de corbes 

    Guitart Morales, Xavier (Publicacions i Edicions de la Universitat de Barcelona (UB), 2008-01-31)
    Part of book or chapter of book
    Open Access