1,721,068 research outputs found
Anticycotomic Iwasawa's Main Conjecture for Hilbert modular forms
Full text linkLet F be a totally real extension and f an Hilbert modular cusp form of level n, with trivial central character and parallel weight 2, which is an eigenform for the action of the Hecke
algebra. Fix a prime P of F of residual characteristic p. Let K be a quadratic totally imaginary extension of F and K' be the P-anticyclotomic Zp-extension of K. The main result
of this paper, generalizing the analogous result of Bertolini and Darmon, states that, under suitable arithmetic assumptions and some technical restrictions, the characteristic power series of the Pontryagin dual of the Selmer group attached of f over K' divides the p-adic L-function attached to f and K' thus proving one direction of the Anticyclotomic Main Conjecture for Hilbert modular forms. Arithmetic applications are given
Quaternionic darmon points on abelian varieties
Full text link[email protected] In the first part ofthe paper we prove formulasfor the p-Adic logarithm of quaternionic Darmon points on modular abelian varieties over Q with toric reduction at p. These formulas are amenable to explicit computations and are the first to treat Stark-Heegner type points on higher-dimensional abelian varieties. In the second part of the paper we explain how these formulas, together with a mild generalization of results of Bertolini and Darmon on Hida families of modular forms and rational points, can be used to obtain rationality results over genus fields of real quadratic fields for Darmon points on abelian varieties
On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations
No full textAresultduetoR.Greenberggivesarelationbetweenthe cardinalityof Selmergroupsof ellipticcurvesovernumberfieldsand thecharacteristicpowerseriesofPontryagindualsofSelmergroupsover cyclotomicZp-extensionsatgoodordinaryprimesp.WeextendGreenberg’sresulttomoregeneralp-adicGaloisrepresentations, includinga largesubclassof thoseattachedtop-ordinarymodular formsofweight at least4andlevelΓ0(N)withp N
Kohnen’s formula and a conjecture of Darmon and Tornaría
Full text linkWe generalize a result of W. Kohnen (1985) to explicit Waldspurger lifts constructed by E. M. Baruch and Z. Mao (2007). As an application, we prove a conjecture formulated by H. Darmon and G. Tornaría (2008)
On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields
Full text linkLet E/F be a modular elliptic curve defined over a totally real number field F and let φ be its associated eigenform. This article presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of E over suitable quadratic imaginary extensions K/F. In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when [F : Q] is even and φ not new at any prime
Euler systems obtained from congruences between Hilbert modular forms
No full textThis paper presents a generalization of the Euler systems considered in [BD2] to the context of Hilbert modular forms. Arithmetic applications are given
Quaternionic Darmon points on abelian varieties
No full text[email protected] In the first part ofthe paper we prove formulasfor the p-Adic logarithm of quaternionic Darmon points on modular abelian varieties over Q with toric reduction at p. These formulas are amenable to explicit computations and are the first to treat Stark-Heegner type points on higher-dimensional abelian varieties. In the second part of the paper we explain how these formulas, together with a mild generalization of results of Bertolini and Darmon on Hida families of modular forms and rational points, can be used to obtain rationality results over genus fields of real quadratic fields for Darmon points on abelian varieties
THE Lambda-ADIC SHIMURA-SHINTANI-WALDSPURGER CORRESPONDENCE
Full text linkWe generalize the Λ-adic Shintani lifting for GL2(Q) to indefinite quaternion algebras over Q
Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case
Full text linkIwasawa theory of modular forms over anticyclotomic Zp-extensions of imaginary quadratic fields K has been studied by several authors, starting from the works of Bertolini–Darmon and Iovita–Spiess, under the crucial assumption that the prime p is unramified in K. We start in this article the systematic study of anticyclotomic p-adic L-functions when p is ramified in K. In particular, when f is a weight 2 modular form attached to an elliptic curve E/Q having multiplicative reduction at p, and p is ramified in K, we show an analogue of the exceptional zeroes phenomenon investigated by Bertolini–Darmon in the setting when p is inert in K. More precisely, we consider situations in which the p-adic L-function Lp(E/K) of E over the anticyclotomic Zp-extension of K does not vanish identically but, by sign reasons, has a zero at certain characters χ of the Hilbert class field of K. In this case we show that the value at χ of the first derivative of Lp(E/K) is equal to the formal group logarithm of the specialization at p of a global point on the elliptic curve (actually, this global point is a twisted sum of Heegner points). This generalizes similar results of Bertolini–Darmon, available when p is inert in K and χ is the trivial character
Galois structure on integral valued polynomials
Full text linkWe characterize finite Galois extensions of the field of rational numbers in terms of the rings of integral valued polynomials recently introduced by Loper and Werner, consisting of those polynomials which have coefficients in Q and such that and take the ring of integers of the Galois extension to itself
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