On the $p$-adic distance between a
point of finite order and a curve of genus higher or equal to
two. [May 2008] This is an effective version of the
Tate-Voloch conjecture for curves embedded in their jacobians, in
a global situation. We combine the local results of Buium with
some global Arakelov-theoretic methods, like Moret-Bailly's
extension of the theorem of the cube.
Note: As R. de Jong pointed out to us, many of the results in this
article can (and should) be improved.
Twisted Frobenius bounds in the smooth and projective case (according to E. Hrushovski). These are the notes of a talk I gave at the CIRM during the meeting "The geometry of the Frobenius automorphism" (which took place during the last week of March 2013). The prerequisites are algebraic geometry at the level of the three first chapters of Hartshorne’s book on algebraic geometry.
Wittgenstein,
l'intuitionisme et le principe du tiers exclu. Exposé fait
le 12 décembre 2013 pendant la Journée d'étude sur la négation
à l'université de Toulouse II.
Quatre exposés faits en fin mars 2013 dans le cadre du groupe de
travail 'Mathématiques et Philosophie Contemporaines'. Le thème
général des exposés était: 'La crise des fondements de
mathématiques. Retour sur certaines problématiques à la lumière de
la philosophie de Wittgenstein.'
(I) Le problèmes des ‘…’. (II) Qu’est-ce qu’une tautologie ?
(III) Retour sur ‘What numbers could
not be’ de P. Benacerraf. (IV) Ce que les énoncés mathématiques
‘veulent dire’.
Autour de la hauteur de Néron-Tate
sur les courbes elliptiques. Ce texte a été rédigé en 2002.
On montre comment diverses formules classiques (entre autres
celles de Tate) peuvent être démontrées directement via la
théorie d'Arakelov.
(with F. Charles) Local
invariance of correspondences at the boundary. This is a
note where we give an independent proof of a local invariance
result also proved in the first paragraph of the following article
by Y. Varshavsky.
Invariance properties of residue
maps in motivic cohomology. In this text, we prove that
residue maps in motivic cohomology satisfy some elementary
invariance properties. This material is certainly well-known to
the experts but it is difficult to find a coherent account of it
in the literature.