I will try to collect some papers here from the time when I thought an elliptic curve was a proper smooth morphism of schemes whose fibers are curves of genus one, together with a distinguished section. Note that all of these papers are in French.

  • Around Serre’s ε conjecture [pdf].
    A short introduction to a result by Mazur and Ribet that plays an important role in Wiles’ proof of Fermat’s last theorem.

  • Construction of a semistable model for certain Siegel varieties [pdf].
    How de Jong and Genestier constructed a semistable resolution for the genus g Siegel variety with Γ0(p) level structure for g = 2 and 3 respectively. One of the less sexy aspects of my Research M.Sc. work.

  • The Picard scheme and elliptic curves [pdf].
    A talk I gave during Y. Laszlo’s algebraic geometry seminar. It presents some properties of the Picard scheme and an elementary application of it.

  • Clifford modules and K-theory [pdf].
    My maîtrise (first M.Sc.) thesis. Joint work with Damien Robert under François Pierrot.

  • An elementary special case of Dirichlet’s theorem [pdf].
    A little note I wrote for my students regarding a problem I gave them, with various developments towards Galois theory and the Chebotarev theorem.

  • The Weil conjectures [pdf].
    An introduction to the Weil conjectures, presented at the entrance competition to ENS.

  • Reciprocity laws [pdf].
    An introduction to algebraic number theory and the notion of “reciprocity laws”, also presented at the entrace competition to ENS.