Recent Submissions

  • 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 ...
  • Del Pezzo surfaces over finite fields and their Frobenius traces 

    Banwait, Barinder; Fite Naya, Francesc; Loughran, Daniel (2018-04-10)
    Article
    Open Access
    Let S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases ...
  • Hopf Galois structures on symmetric and alternating extensions 

    Río Doval, Ana; Vela del Olmo, Maria Montserrat; Crespo Vicente, Teresa (2018)
    Article
    Open Access
    By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric ...
  • Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture 

    Longo, Matteo; Rotger Cerdà, Víctor; Vera Piquero, Carlos de (2018-01-01)
    Article
    Open Access
    We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternionic orders. We address several questions ...
  • Computation of numerical semigroups by means of seeds 

    Bras Amorós, Maria; Fernández González, Julio (2018-09-01)
    Article
    Open Access
    For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of seed by broadening the notion of generator. This new concept allows us to explore the semigroup tree in ...
  • Stark points and p-adic iterated integrals attached to modular forms of weight one 

    Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (Cambridge University Press, 2015-01-01)
    Article
    Open Access
    Let be an elliptic curve over , and let and be odd two-dimensional Artin representations for which is self-dual. The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms , , and ...
  • Beilinson-Flach elements and Euler systems II: p-adic families and the Birch and Swinnerton-Dyer conjecture 

    Bertolini, Massimo; Darmon, Henri; Rotger Cerdà, Víctor (2015-03-23)
    Article
    Open Access
    Let E be an elliptic curve over Q and let % be an odd, irreducible twodimensional Artin representation. This article proves the Birch and Swinnerton-Dyer conjecture in analytic rank zero for the Hasse-WeilArtin L-series ...
  • Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one 

    Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (2016-08-01)
    Article
    Open Access
    This article can be read as a companion and sequel to the authors’ earlier article on Stark points and p-adic iterated integrals attached to modular forms of weight one, which proposes a conjectural expression for the ...
  • Elliptic curves of rank two and generalized Kato classes 

    Darmon, Henri; Rotger Cerdà, Víctor (2016-08-24)
    Article
    Open Access
    Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-series. ...
  • On the rank and the convergence rate toward the Sato-Tate measure 

    Fite Naya, Francesc; Guitart Morales, Xavier (2017-10-16)
    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 ...
  • Stark points and the Hida-Rankin p-adic L-function 

    Casazza, Daniele; Rotger Cerdà, Víctor (2018-02)
    Article
    Open Access
    This article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental part of a p-adic avatar of the leading term at s=1 of the Hasse–Weil–Artin ...
  • On the Sato-Tate conjecture for non-generic abelian surfaces 

    Johansson, Christian; Fite Naya, Francesc (2017-01)
    Article
    Open Access
    We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fité, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.

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