00:00:00 / 00:00:00

The generalized Sato-Tate conjecture

By Francesc Fité

Appears in collection : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes

This series of three talks is the first part of an introductory course on the generalized Sato-Tate conjecture, made in collaboration with Andrew V. Sutherland at the Winter School "Frobenius distributions on curves", celebrated in Luminy in February 2014. In the first talk, some general background following Serre's works is introduced: equidistribution and its connexion to L-functions, the Sato-Tate group and the Sato-Tate conjecture. In the second talk, we present the Sato-Tate axiomatic, which leads us to some Lie group theoretic classification results. The last part of the talk is devoted to illustrate the methods involved in the proof of this kind of results by considering a concrete example. In the third and final talk, we present Banaszak and Kedlaya's algebraic version of the Sato-Tate conjecture, we describe the notion of Galois type of an abelian variety, and we establish the dictionary between Galois types and Sato-Tate groups of abelian surfaces defined over number fields. generalized Sato-Tate conjecture - Sato-Tate group - equidistribution - Sato-Tate axioms - Galois type - Abelian surfaces - endomorphism algebra - Frobenius distributions

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.18605003
  • Cite this video Fité Francesc (2/17/14). The generalized Sato-Tate conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18605003
  • URL https://dx.doi.org/10.24350/CIRM.V.18605003

Domain(s)

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback