Séminaire Arithmétique et géométrie algébrique
organisé par l'équipe Arithmétique et géométrie algébrique
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Livia Grammatica
Tate-linear formal varieties
15 janvier 2026 - 14:00Salle de séminaires IRMA
We work over a closed field of positive characteristic. A classic result of Serre-Tate says that the deformation space of an ordinary abelian variety has the structure of a formal torus, and one can consider the closed subvarieties which are given by formal subtori. Tate-linear formal varieties play the role of formal subtori in the deformation space of abelian varieties of arbitrary Newton polygon. Recent work of Chai-Oort established an important link between Tate-linear subvarieties and the Hecke orbit conjecture for \mathcal{A}_g, which then led to a full solution for Shimura varieties of Hodge type by D'Addezio and van Hoften. We will explain the role of Tate-linear varieties in the Hecke orbit conjecture, their conjectural link with special subvarieties of \mathcal{A}_g, and show how p-adic monodromy techniques can help shed light on their structure. -
Lin Zhou
On the infinite generation of morphic and motivic cohomology
22 janvier 2026 - 14:00Salle de séminaires IRMA
Since Mumford’s work in the 1960s, questions on the finite generation of Chow and Griffiths groups—such as the finiteness of dimension, the size of their torsion, or their divisibility—have been a central theme in the study of algebraic cycles. Motivic cohomology and morphic cohomology naturally generalize the Chow group (cycles modulo rational equivalence) and cycles modulo algebraic equivalence. In this talk, I will show how, over an algebraically closed field whose transcendence degree over its prime field is infinite (e.g., the complex number field), one can combine Schoen’s injectivity argument with Schreieder’s refined unramified cohomology to construct examples of motivic and morphic cohomology groups with infinitely many torsion elements. These appear to be the first known examples exhibiting infinite torsion in motivic or morphic cohomology. Joint work with Theodosis Alexandrou.