Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Ratazzi, Nicolas"'
Autor:
Hindry, Marc, Ratazzi, Nicolas
Publikováno v:
Algebra Number Theory 10 (2016) 1845-1891
Let A be an abelian variety defined over a number field K, the number of torsion points rational over a finite extension L is bounded polynomially in terms of the degree [L : K]. When A is isogenous to a product of simple abelian varieties of type I
Externí odkaz:
http://arxiv.org/abs/1505.05620
Autor:
Ratazzi, Nicolas
Cette thèse est consacrée aux problèmes de minorations de hauteur normalisée des points et des sous-variétés non de torsion. Le chapitre 1 est un chapitre de rappels, les autres sont originaux. On prouve au chapitre 2 un résultat de densité d
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00006163
http://tel.archives-ouvertes.fr/docs/00/04/68/39/PDF/tel-00006163.pdf
http://tel.archives-ouvertes.fr/docs/00/04/68/39/PDF/tel-00006163.pdf
Autor:
Ratazzi, Nicolas
Faltings in 1983 proved that a necessary and sufficient condition for two abelian varieties $A$ and $B$ to be isogenous over a number field $K$ is that the local factors of the L-series of $A$ and $B$ are equal for almost all primes of $K$ ; for each
Externí odkaz:
http://arxiv.org/abs/1211.4387
Autor:
Hindry, Marc, Ratazzi, Nicolas
Let $A$ be an abelian variety defined over a number field $K$, the number of torsion points rational over a finite extension $L$ is bounded polynomially in terms of the degree $[L:K]$. When $A$ is isogenous to a product of simple abelian varieties of
Externí odkaz:
http://arxiv.org/abs/0911.5505
Autor:
Hindry, Marc, Ratazzi, Nicolas
Let $A$ be an abelian variety defined over a number field $K$, the number of torsion points rational over a finite extension $L$ is bounded polynomially in terms of the degree $[L:K]$. We formulate a question suggesting the optimal exponent for this
Externí odkaz:
http://arxiv.org/abs/0804.3031
Autor:
Nakamaye, Michael, Ratazzi, Nicolas
We establish an improvement of Philippon's zero estimates primarily in the multiplicity setting. The improvement is made possible by a more geometric approach and in particular the use of Seshadri constants.
Comment: 17 pages, final version, acc
Comment: 17 pages, final version, acc
Externí odkaz:
http://arxiv.org/abs/math/0605730
Autor:
Ratazzi, Nicolas
We prove a special case of the following conjecture of Zilber-Pink generalising the Manin-Mumford conjecture : let $X$ be a curve inside an Abelian variety $A$ over $\bar{\Q}$, provided $X$ is not contained in a torsion subvariety, the intersection o
Externí odkaz:
http://arxiv.org/abs/math/0502186
Autor:
Ratazzi, Nicolas
Let A be an abelian variety of dimension g defined over a number field K. We study the size of the torsion group A(F)_{tors} where F/K is a finite extension and more precisely we study the possible exponent \gamma in the inequality Card(A(F)_{tors})<
Externí odkaz:
http://arxiv.org/abs/math/0502185
Autor:
Ratazzi, Nicolas
Let $A/K$ be an abelian variety over a number field $K$. We prove in this article that a good lower bound (in terms of the degree $[K(P):K]$) for the N\'eron-Tate height of the points $P$ of infinite order modulo every strict abelian subvarieties of
Externí odkaz:
http://arxiv.org/abs/math/0402225
Autor:
Ratazzi, Nicolas
Let E/K be an elliptic curve with complex multiplication and let $K^{ab}$ be the Abelian closure of $K$. We prove in this article that there exists a constant $c(E/K)$ such that : for all point $P\in E(\bar{K})-E_{tors}$, we have \[\hat{h}(P)\geq\fra
Externí odkaz:
http://arxiv.org/abs/math/0402224