On L-functions of elliptic curves and cyclotomic towers.
On -adic -functions
On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.
On the Birch and Swinnerton-Dyer conjecture
On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields
Let be a modular elliptic curve defined over a totally real number field and let be its associated eigenform. This paper presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of over suitable quadratic imaginary extensions . In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when is even and not new at any prime.
On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristic p > 0.
On the conjectures of Birch and Swinnerton-Dyer and a geometric analog
On the de Rham and -adic realizations of the elliptic polylogarithm for CM elliptic curves
In this paper, we give an explicit description of the de Rham and -adic polylogarithms for elliptic curves using the Kronecker theta function. In particular, consider an elliptic curve defined over an imaginary quadratic field with complex multiplication by the full ring of integers of . Note that our condition implies that has class number one. Assume in addition that has good reduction above a prime unramified in . In this case, we prove that the specializations of the -adic elliptic...
On the ...-factor attached to motives.
On the leading terms of zeta isomorphisms and -adic -functions in non-commutative Iwasawa theory.
On the meromorphic continuation of degree two -functions.
On the p-adic height of Heegner cycles.
On the parity of ranks of Selmer groups. III.
On the values of Artin L-series at s=1 and annihilation of class groups
Let L be a finite Galois CM-extension of a totally real field K. We show that the validity of an appropriate special case of the Equivariant Tamagawa Number Conjecture leads to a natural construction for each odd prime p of explicit elements in the (non-commutative) Fitting invariants over of a certain tame ray class group, and hence also in the analogous Fitting invariants of the p-primary part of the ideal class group of L. These elements involve the values at s=1 of the Artin L-series of characters...
On the values of equivariant zeta functions of curves over finite fields.
On the vanishing of twisted -functions of elliptic curves.
On the -factors of motives. II.
-adic Fourier theory.
-adic representations arising from descent on abelian varieties
Points entiers et théorèmes de Bertini arithmétiques
On décrit dans cet article une version effective d’un théorème de Rumely : on peut trouver beaucoup de points entiers sur des ouverts (assez grands) de variétés arithmétiques, tout en contrôlant la hauteur de ces points. On applique ensuite ce résultat :- aux modèles de variétés abéliennes;- à la démonstration d’un analogue arithmétique des théorèmes de Bertini.