Unpublished texts

(with V. Maillot) A conjecture on the equivariant analytic torsion forms. Letter sent to J.-M. Bismut and X. Ma on Dec. 21st 2005.
Note: J.-M. Bismut made it clear to the authors of the above letter that there is no good reason why the conjectures made therein should be true. The authors have not yet been able to make any more convincing conjectures.

Riemann-Roch formulae in Arakelov geometry and applications. Notes of a minicourse given at the CRM in Barcelona (Spain) during the last week of February 2006.

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.

On abelian varieties with an infinite group of separable $p^\infty$-torsion points. This is a note written for J.-F. Voloch in 2012. We give a statement, which improves on Th. 1.4 in my article Infinitely p-divisible points on abelian varieties defined over function fields of characteristic p>0, which appeared in Notre Dame Journal of Formal Logic 54 (2013),  no. 3-4, 579--589.

Deux exposés faits dans le cadre de l'école thématique « Mathématique, Informatique et Philosophie Contemporaines » III, Toulouse, 23-27 mars 2015. Un aperçu de la philosophie des sciences de F. Gonseth et L'objet mathématique à la lumière de l'existentialisme thomiste.

[NEW] The development of mathematical theories. A few remarks. Talk given on 16th April 2016 in the framework of the workshop Mathematics & Philosophy of Mathematics (Toulouse, Université Paul-Sabatier, 15-16 April 2016).