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.