If you're looking for my professional Web site, it is elsewhere.
As the title indicates, this is my “old” math page. It is a repertoire of various mathematical texts I wrote when I was student (at the ENS essentially, or before), which I keep for its “historical” interest (some people find certain things on this page interesting for various reasons, so I don't want to simply remove it from the Web). This is not my current mathematical research, only old stuff: for my publication list and whatnot, please see my professional Web site (which is also not up to date, unfortunately).
For the same reason, I am generally not interested in possible errors in these papers: I know there are some, but this is old stuff, and the style of TeX and the mode of compilation is such that it would be very inconvenient for me to make any changes now (in a few cases, I may even have lost the source).
There are more math pages on this site, some being possibly more up to date than this one (such as the math posts on my blog).
See my professional Web site.
My doctoral dissertation, done under Jean-Louis Colliot-Thélène's supervision, entitled Hypersurfaces cubiques : équivalence rationnelle, R-équivalence et approximation faible (pdf)
My magistère dissertation includes a copy of both my master's dissertation and my DEA dissertation (below). It also contains a simplified presentation of the latter as well as a few notes on intuitionist logic as a kind of summary of the workshop I organised on the subject last year. (ps (compressed); French and English)
My DEA dissertation, done under Michel
supervision, in which I prove two results of Raynaud's on theta
divisors, and ordinarity of curves and coverings. Actually, this
paper is not strictly my DEA dissertation, but the text of a talk I
gave a month later at the CIRM in Luminy on the same subject. (LaTeX, dvi or ps (compressed); English)
My master's dissertation, done jointly with
Jean Marot (
under Yves Laszlo's (
supervision on Belyj's theorem (concerning
étale coverings of the projective line minus three points).
I have organized at the ENS a workshop on logic, set theory and forcing (both classical and intuitionist) during the 1998–1999 term. Here is the list of talks that took place:
I have written a rather long sequence of thoughts on the hypothetical theory of noncommutative algebraic geometry. Now I don't agree with all these thoughts any more (and in particular I think that my emphasis on a non-symmetry-breaking way of doing things is stupid — though I still agree with what I said about the category of rings having unsatisfactory colimits). Anyway, here are most of these thoughts (in order of decreasing interest):
A newer programme for algebraic geometry was posted more recently to that same newsgroup.
Some posts I made to the students' forum (local newsgroup) of the ENS, included in my Best Of are of mathematical interest (note that all are in French):
What follows was written a long time ago (before I entered the ENS, essentially), and may be hopelessly wrong, out of date, or anything like that: caveat sumptor.
If you don't know about the French educational system, the above word means “glue” (with a very strange spelling — something like “ghloo”) and refers to an oral interrogation. Anyway, I used to be a “khôlleur” and you can find the list of exercices I gave on the French version of this page (they are all in French, naturally).
The same comment as above applies here. DEUG refers to the first two years of University (i.e. undergraduate years) in France; MIAS means “Mathematics, Informatics (i.e. computer science) and Applications to Sciences”. Since september 2000, I teach in DEUG MIAS. I have written a few complete solutions to various exercices: see the French version of this page.