L-functions and periods of polarized regular motives.
L-functions of elliptic curves with complex multiplication, I
L-functions of elliptic curves with complex multiplication, II
Lifting Galois representations and a conjecture of Fontaine and Mazur.
Line bundles on arithmetic surfaces and intersection theory.
Linear independence of linear forms in polylogarithms
For , , , let be the -th polylogarithm of . We prove that for any non-zero algebraic number such that , the -vector space spanned by has infinite dimension. This result extends a previous one by Rivoal for rational . The main tool is a method introduced by Fischler and Rivoal, which shows the coefficients of the polylogarithms in the relevant series to be the unique solution of a suitable Padé approximation problem.
Lineare rekurrente Folgen auf elliptischen Kurven
Links between cyclotomic and Iwasawa theory.
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 height functions and the Mordell-Weil theorem for Drinfeld modules
Local heights on Abelian varieties and rigid analytic uniformization.
Local heights on Galois covers of the projective line
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-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.
Local-global principle for Witt equivalence of function fields over global fields
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...
Logarithmic derivatives of Dirichlet -functions and the periods of abelian varieties
Loi de réciprocité quadratique dans les corps quadratiques imaginaires
À partir d’une courbe elliptique définie sur le corps des classes de Hilbert d’un corps quadratique imaginaire et à multiplicité complexe par l’anneau des entiers de , on construit des fonctions elliptiques. Nous établissons des formules produits relatives à ces fonctions. De ce fait, nous obtenons une formulation analytique du lemme de Gauss généralisé ainsi qu’une expression explicite pour le symbole quadratique de Legendre défini sur l’anneau des entiers du corps quadratique imaginaire. Comme...
Lower Bounds for Heights on Finitely Generated Groups.
Lower bounds of heights of points on hypersurfaces
Lower bounds on the projective heights of algebraic points