Now showing items 1-16 of 16

    • Algorithms for chow-heegner points via iterated integrals 

      Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger Cerdà, Víctor (2015)
      Article
      Restricted access - publisher's policy
      Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of ...
    • Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes 

      Molina Blanco, Santiago; Rotger Cerdà, Víctor (2014)
      Article
      Open Access
      The aim of this short note is to show how the interplay of the action of the automorphism group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction and its sets ...
    • Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series 

      Bertolini, Massimo; Darmon, Henri; Rotger Cerdà, Víctor (2015)
      Article
      Open Access
      This article is the first in a series devoted to the Euler system arising from p-adic families of Beilinson-Flach elements in the first K-group of the product of two modular curves. It relates the image of these elements ...
    • 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 ...
    • Beilinson-Flach elements, Stark units and p-adic iterated integrals 

      Rivero Salgado, Óscar; Rotger Cerdà, Víctor (2019-08-14)
      Article
      Open Access
      We study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in ...
    • Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions 

      Darmon, Henri; Rotger Cerdà, Víctor (2017-07-01)
      Article
      Open Access
      This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension ...
    • 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. ...
    • 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 ...
    • 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 ...
    • Heegner points, Stark-Heegner points and diagonal classes 

      Bertolini, Massimo; Darmon, Henri; Rotger Cerdà, Víctor; Seveso, Marco Adamo; Venerucci, Rodolfo (2020-02-03)
      Book
      Restricted access - publisher's policy
    • On rigid analytic uniformizations of Jacobians of Shimura curves 

      Longo, Matteo; Rotger Cerdà, Víctor; Vigni, Stefano (2012)
      Article
      Open Access
      The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed ...
    • On the elliptic Stark conjecture at primes of multiplicative reduction 

      Casazza, Daniele; Rotger Cerdà, Víctor (2019-01-01)
      Article
      Open Access
      In [DLR], Darmon, Lauder, and Rotger formulated a p-adic elliptic Stark conjecture for the twist of an elliptic curve E/Q by the self-dual tensor product ¿ ¿ of two odd and two-dimensional Artin representations. These ...
    • Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields 

      Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor (2015-10-01)
      Article
      Restricted access - publisher's policy
      This article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the ...
    • Sato-Tate distributions and Galois endomorphism modules in genus 2 

      Fité, Francesc; Kedlaya, Kiran; Rotger Cerdà, Víctor; Sutherland, Andrew (2012)
      Article
      Restricted access - publisher's policy
      For an abelian surface A over a number eld k, we study the limit- ing distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to taking characteristic poly- nomials ...
    • 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 ...
    • 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 ...