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Séminaire Arithmétique et géométrie algébrique

organisé par l'équipe Arithmétique et géométrie algébrique

  • Marco Robalo

    HKR theorems and exponentials

    3 avril 2025 - 14:00Salle de séminaires IRMA

    In this talk we will explain a computation describing Hochschild-Kostant-Rosenberg isomorphism theorems as exponential maps. This computation uses the construction of a filtered circle obtained in collaboration with Moulinos and Toën. As two independent applications we will discuss a definition of motivic Donaldson-Thomas invariants in positive characteristic and the extension of Hochschild homology for elliptic curves.

  • Hélène Esnault

    À déterminer

    11 avril 2025 - 14:00Salle de séminaires IRMA

  • Hélène Esnault

    Vanishing at the generic point in cohomology

    11 avril 2025 - 14:00Salle de séminaires IRMA

    (1.5-hour talk) If X is a smooth projective variety defined over the field of complex numbers, its i-th Betti cohomology H^i(X, \mathbb C) is said to have coniveau one if there is a Zariski dense open U \subset X such that the restriction map H^i(X,\mathbb C) \to H^i(U,\mathbb C) dies. Equivalently, the restriction map to the generic point of X in i-th cohomology vanishes. Grothendieck’s generalized Hodge conjecture is in general difficult to express as one needs the notion of Hodge sub-structure, but one particular instance has a purely algebraic formulation. It predicts that if X has no non-trivial global differential forms of degree i, then H^i(X, \mathbb C) should have coniveau one. The converse is easily seen to be true. Aside of i=1,2, for which complex Hodge theory gives a positive answer, we know nothing. On the other hand, the philosophy behind is very useful to draw analogies, e.g. it helps to find rational points over finite fields of rationally connected varieties (Lang-Manin conjecture). So it is worth to try to understand whether more modern p-adic methods yield some non-trivial information. With Mark Kisin and Alexander Petrov, in work in progress, we formulate and prove a vanishing result in the separate quotient of p-completed de Rham cohomology, and a weaker version in the separate quotient of prismatic cohomology. I’ll present the ‘program’ and a few questions which at present are not understood.

  • Matteo Penegini

    TBA

    24 avril 2025 - 14:00Salle de séminaires IRMA

  • Pol Van Hoften

    À déterminer

    28 mai 2025 - 14:00Salle de séminaires IRMA

  • Philip Severin

    TBA

    12 juin 2025 - 14:00Salle de séminaires IRMA