• Abelian varieties with many endomorphisms and their absolutely simple factors 

    Guitart Morales, Xavier (2012)
    Article
    Accés restringit per política de l'editorial
    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
    Accés restringit per política de l'editorial
    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, ...
  • Modular abelian varieties over number fields 

    Guitart Morales, Xavier; Quer Bosor, Jordi (2014)
    Article
    Accés restringit per política de l'editorial
    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
    Accés obert
    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 ...
  • Parametrization of Abelian K-surfaces with quaternionic multiplication 

    Guitart Morales, Xavier; Molina Blanco, Santiago (2009-12)
    Article
    Accés restringit per política de l'editorial
    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)
    Capítol de llibre
    Accés obert