L-Functions and Division Towers.
L-functions and periods of polarized regular motives.
L-functions of elliptic curves with complex multiplication, I
L-functions of p-adic characters and geometric Iwasawa theory.
L’hyperanneau des classes d’adèles
J’exposerai ici quelques résultats récents (obtenus en collaboration avec C. Consani [3], [4], [5], [6]) qui portent sur le cas limite de la “caractéristique ”. Le but principal est de montrer que l’espace des classes d’adèles d’un corps global, qui jusqu’à présent n’a été considéré que comme un espace (non-commutatif), admet en fait une structure algébrique naturelle. Nous verrons également que la construction de l’anneau de Witt d’un anneau de caractéristique admet un analogue en caractéristique...
Lifting Witt subgroups to characteristic zero.
Line bundles on arithmetic surfaces and intersection theory.
Linear forms on abelian varieties over local fields
Lines on del Pezzo surfaces with in characteristic 2 in the smooth case.
Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer
Local and canonical heights of subvarieties
Classical results of Weil, Néron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the -product of Gillet-Soulé developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using methods from...
Local Diophantine Properties of Shimura Curves.
Local heights on Abelian varieties and rigid analytic uniformization.
Local heights on Momford curves.
Local Indecomposability of Hilbert Modular Galois Representations
We prove the indecomposability of the Galois representation restricted to the -decomposition group attached to a non CM nearly -ordinary weight two Hilbert modular form over a totally real field under the assumption that either the degree of over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of .
Local L-factors of motives and regularized determinants.
Local monodromy in non-archimedean analytic geometry
Local units, elliptic units, Heegner points and elliptic curves.
Local-global divisibility of rational points in some commutative algebraic groups
Let be a commutative algebraic group defined over a number field . We consider the following question:Let be a positive integer and let . Suppose that for all but a finite number of primes of , we have for some . Can one conclude that there exists such that ?A complete answer for the case of the multiplicative group is classical. We study other instances and in particular obtain an affirmative answer when is a prime and is either an elliptic curve or a torus of small dimension...
Local-global principle for certain biquadratic normic bundles
Let X be a proper smooth variety having an affine open subset defined by the normic equation over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.