The book surveys some recent developments in the arithmetic of modular elliptic curves. It
places a special emphasis on the construction of rational points on elliptic curves, the Birch …

This article describes a conjectural p-adic analytic construction of global points on (modular)
elliptic curves, points which are defined over the ring class fields of real quadratic fields. The …

In Bull. Soc. Math. France 115 (1987), 399–456, Perrin-Riou formulates a form of the
Iwasawa main conjecture which relates Heegner points to the Selmer group of an elliptic …

Hida families and rational points on elliptic curves Page 1 DOI: 10.1007/s00222-007-0035-4
Invent. math. 168, 371–431 (2007) Hida families and rational points on elliptic curves Massimo …

Si M est un motif défini sur un corps de nombres, on sait lui associer (au moins
conjecturalement) une fonction analytique complexe L (M, s) définie par un produit eulérien …

Elliptic units, which are obtained by evaluating modular units at quadratic imaginary
arguments of the Poincar? upper half-plane, provide us with a rich source of arithmetic …

Abstract In an earlier paper [10], Howard proved one divisibility of Perrin-Riou's Iwasawa
main conjecture for Heegner points on elliptic curves. In this paper, that result is generalized …

Let G be the group (GL 2× GU (1))/GL 1 over a totally real field F, and let X be a Hida family
for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of …

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 $\Bbb {Q} $ at a prime dividing exactly …

We propose a refined version of the Beilinson–Bloch conjecture for the motive associated
with a modular form of even weight. This conjecture relates the dimension of the image of …