Derived Seminar

vendredi 16 oct. 2026, 13:45 → 17:30 Europe/Paris

Amphithéâtre Yvonne Choquet-Bruhat (IHP - Bâtiment Perrin)

13:45 → 15:30 Binomial algebraic geometry and homotopy theory

I will explain an idea of Grothendieck set out in "Pursuing Stacks" for faithfully encoding homotopy types in higher binomial stacks. These higher binomial stacks are analogous to stacks in classical algebraic geometry, but the commutative ring structure is replaced by that of a binomial ring (a ring in which generalized binomial coefficients are defined). As an application of this theory, I will explain how one can construct an action of a motivic Galois group on certain homotopy types.

Orateur: Geoffroy Horel (Sorbonne Université)

15:45 → 17:30 Solid Syntomifications

To a p-adic formal scheme, one can associate its prismatic or syntomic cohomology. These are cohomology theories that refine the crystalline cohomology of the special fiber and the p-adic etale cohomology of the generic fiber. After these cohomology theories were found by Bhatt-Morrow-Scholze and Bhatt-Scholze, Bhatt-Lurie and Drinfeld gave an interpretation in terms of quasi-coherent cohomology on certain stacks, which, in particular, equips those theories with coefficient systems. In this talk, I will explain how to extend these coefficient systems to well-behaved six-functor formalisms by giving possible interpretations of the stacks of Bhatt-Lurie and Drinfeld as analytic stacks (in the sense of Clausen-Scholze). We will discuss advantages and disadvantages of these different incarnations and why this additional step to analytic stacks is necessary.

Orateur: Niklas Kipp (Université d'Orsay)