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Séminaire Arithmétique et géométrie algébrique

organisé par l'équipe Arithmétique et géométrie algébrique

  • Andrea Gallese

    How to compute the connected monodromy field of a CM abelian variety

    2 avril 2026 - 14:00Salle de séminaires IRMA

    Let A be an abelian variety defined over a number field k. The connected monodromy field k(eA) is the minimal extension of k over which every \ell-adic Galois representation attached to A has connected image, or equivalently, the minimal extension over which all Tate classes on all self-products A^r are defined. When k(eA)/k(End A) has positive degree, "exotic" Tate classes arise on certain powers A^r — classes not explained by the endomorphism algebra alone. I will explain how to compute k(eA) when A is the Jacobian of a curve with complex multiplication. We will exploit CM theory to describe the algebra of Tate classes and make the Galois action on this algebra explicit in terms of periods — suitable integrals of algebraic differential forms. Though periods are generally transcendental, those attached to Tate classes are algebraic, so computing k(eA) reduces to identifying these periods as exact algebraic numbers.

  • German Stefanich

    tbd

    9 avril 2026 - 14:00Salle de séminaires IRMA