Séminaire Arithmétique et géométrie algébrique
organisé par l'équipe Arithmétique et géométrie algébrique
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Takumi Watanabe
On the (phi, Gamma)-modules Corresponding to Crystalline Representations and Semi-stable Representations
6 mars 2025 - 14:00Salle de séminaires IRMA
From the 1980s to the 1990s, Jean-Marc Fontaine introduced the theory of (phi, Gamma)-modules to study p-adic Galois representations. They are simpler than p-adic Galois representations, but he showed an equivalence between them. Among p-adic Galois representations, some classes are particularly important in number theory. Main examples are crystalline representations, semi-stable representations and de Rham representations. In this talk, I will explain how we can determine the (phi, Gamma)-modules corresponding to crystalline representations and semi-stable representations. These results can be seen, in a sense, as generalizations of Wach modules. -
Clement Dupont
TBA
13 mars 2025 - 14:00Salle de séminaires IRMA
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Francesca Rizzo
On the geometry of singular EPW cubes
20 mars 2025 - 14:00Salle de séminaires IRMA
EPW cubes are projective hyper-Kähler varieties of dimension 6, constructed by Iliev, Kapustka, Kapustka, and Ranestad. Their construction and behavior share many similarities with the double EPW sextics constructed by O'Grady. Both double EPW sextics and EPW cubes are among the few classes of hyper-Kähler varieties for which it is possible to provide a geometric construction for the general element in their moduli space. In this talk, we will briefly introduce hyper-Kähler varieties and their moduli spaces. We will describe the construction of double EPW sextics and EPW cubes, along with their properties. Finally, we will discuss how, following O'Grady's results, we obtain a hyper-Kähler resolution of singular EPW cubes. -
Alexei Skorobogatov
TBA
27 mars 2025 - 14:00Salle de séminaires IRMA