Browsing by Author "Rotger Cerdà, Víctor"
Now showing items 1-16 of 16
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Algorithms for chow-heegner points via iterated integrals
(2015)
Article
Restricted access - publisher's policyLet 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
(2014)
Article
Open AccessThe 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
(2015)
Article
Open AccessThis 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
(2015-03-23)
Article
Open AccessLet 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
(2019-08-14)
Article
Open AccessWe 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
(2017-07-01)
Article
Open AccessThis 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
(2016-08-24)
Article
Open AccessHeegner 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
(2016-08-01)
Article
Open AccessThis 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
(2018-01-01)
Article
Open AccessWe 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
(2020-02-03)
Book
Restricted access - publisher's policy -
On rigid analytic uniformizations of Jacobians of Shimura curves
(2012)
Article
Open AccessThe 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
(2019-01-01)
Article
Open AccessIn [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
(2015-10-01)
Article
Restricted access - publisher's policyThis 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
(2012)
Article
Restricted access - publisher's policyFor 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
(Cambridge University Press, 2015-01-01)
Article
Open AccessLet 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
(2018-02)
Article
Open AccessThis 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 ...
