Galois representations of octahedral type and 2-coverings of elliptic curves.
Galois theory, elliptic curves, and root numbers
Genres de Todd et valeurs aux entiers des dérivées de fonctions
La géométrie d’Arakelov étudie les fibrés vectoriels sur une variété algébrique définie sur les entiers, munis d’une métrique hermitienne lisse sur le fibré holomorphe associé (sur la variété analytique des points complexes de ). Un théorème de “Riemann-Roch arithmétique” calcule le covolume du réseau euclidien des sections globales d’un tel fibré. Dans cette formule, le genre de Todd comporte un terme complémentaire, défini par une série formelle dont les coefficients font intervenir les valeurs...
Groupe de Selmer d'une courbe elliptique à multiplication complexe
Growth of Selmer groups of Hilbert modular forms over ring class fields
We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.
Heegner points and derivatives of L-series.
Heegner Points and Derivatives of L-Series. II.
Heegner points and -series of automorphic cusp forms of Drinfeld type.
Heights of Heegner points on Shimura curves.
Hida families, -adic heights, and derivatives
This paper concerns the arithmetic of certain -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a -adic regulator, and the derivative of a -adic -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...
Higher order operations in Deligne cohomology.
Higher regulators and Hecke L-series of imaginary quadratic fields I.
Horizontal Factorizations of Certain Hasse-Weil Zeta Functions - a Remark on a Paper by Taniyama
Ideal class group annihilators
Inductivity of the global root number
Under suitable hypotheses, we verify that the global root number of a motivic L-function is inductive (invariant under induction).
Invariance of the parity conjecture for -Selmer groups of elliptic curves in a -extension
We show a -parity result in a -extension of number fields () for the twist : , where is an elliptic curve over , and are respectively the quadratic character and an irreductible representation of degree of , and is the -Selmer group. The main novelty is that we use a congruence result between -factors (due to Deligne) for the determination of local root numbers in bad cases (places of additive reduction above 2 and 3). We also give applications to the -parity conjecture (using...
Investigations of zeros near the central point of elliptic curve -functions (with an appendix by Eduardo Dueñez).
Iwasawa-theory of abelian varieties at primes of non-ordinary reduction.
-functions.
La conjecture de Birch et Swinnerton-Dyer -adique
La conjecture de Birch et Swinnerton-Dyer prédit que l’ordre du zéro en de la fonction d’une courbe elliptique définie sur est égal au rang du groupe de ses points rationnels. On sait démontrer cette conjecture si ou , mais on n’a aucun résultat reliant et si . Nous expliquerons comment Kato démontre que la fonction -adique attachée à a, en , un...