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Dans ce texte on introduit une notion de hauteur pour les sous-schémas d'une variété
arithmétique. Dans le cas particulier d'un sous-schéma de dimension (générique) nulle de
l'espace projectif, on donne pour ces hauteurs une estimation qui prend la forme d'une
formule de Hilbert-Samuel arithmétique, généralisant ainsi des résultats de M. Laurent
sur les hauteurs de matrices d'interpolation. Les trois premiers termes du développement
asymptotique ainsi obtenu peuvent s'analyser...
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of...
We compare general inequalities between invariants of number fields and invariants of elliptic curves over number fields. On the number field side, we remark that there is only a finite number of non-CM number fields with bounded regulator. On the elliptic curve side, assuming the height conjecture of Lang and Silverman, we obtain a Northcott property for the regulator on the set of elliptic curves with dense rational points over a number field. This amounts to say that the arithmetic of CM fields...
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