Icosahedral Galois Extensions and Elliptic Curves.
Ideal class group annihilators
Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves
We study the problem of constructing and enumerating, for any integers , number fields of degree whose ideal class groups have “large" -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
Il n'y a pas de variété abélienne sur Z.
Implementing 2-descent for Jacobians of hyperelliptic curves
Improper Eisenstein Series on Bruhat-Tits Trees.
Improved bounds on the number of low-degree points on certain curves
Improved upper bounds for the number of points on curves over finite fields
We give new arguments that improve the known upper bounds on the maximal number of rational points of a curve of genus over a finite field , for a number of pairs . Given a pair and an integer , we determine the possible zeta functions of genus- curves over with points, and then deduce properties of the curves from their zeta functions. In many cases we can show that a genus- curve over with points must have a low-degree map to another curve over , and often this is enough to...
Indépendance algébrique et exponentielle de Carlitz
Indice des unités elliptiques dans les -extensions
Nous comparons le comportement dans les -extensions du nombre de classes d’idéaux avec le comportement de l’indice du groupe des unités elliptiques de Rubin.
Indices of double coverings of genus 1 over -adic fields
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).
Inégalité de Vojta en dimension supérieure
Inégalité de Vojta généralisée
La méthode que Vojta a introduite dans sa preuve de la conjecture de Mordell et que Faltings a étendue pour prouver la conjecture de Lang sur les sous-variétés de variétés abéliennes repose sur une inégalité de hauteurs obtenue par approximation diophantienne. Nous montrons qu’une telle inégalité peut s’énoncer de manière très générale en dehors du contexte des groupes algébriques. Ce faisant, nous lui conférons également plus de souplesse, ce qui conduit à des applications nouvelles même sur les...
Inegalite relative des genres.
Infinite rank of elliptic curves over
If E is an elliptic curve defined over a quadratic field K, and the j-invariant of E is not 0 or 1728, then has infinite rank. If E is an elliptic curve in Legendre form, y² = x(x-1)(x-λ), where ℚ(λ) is a cubic field, then has infinite rank. If λ ∈ K has a minimal polynomial P(x) of degree 4 and v² = P(u) is an elliptic curve of positive rank over ℚ, we prove that y² = x(x-1)(x-λ) has infinite rank over .
Integer Points and the Rank of Thue Elliptic Curves.
Integer points on curves of genus 1
Integer points unusually close to elliptic curves.
Integral canonical models of Shimura varieties
The aim of these notes is to provide an introduction to the subject of integral canonical models of Shimura varieties, and then to sketch a proof of the existence of such models for Shimura varieties of Hodge and, more generally, abelian type. For full details the reader is refered to [Ki 3].