This is the homepage of the Motives Seminar, an irregular seminar at Orsay on K-theory, arithmetic geometry, cohomology theories, localising invariants, algebraic cycles, motives (commutative and non-commutative), etc.
The seminar meets occasionally on Monday afternoons at 2pm, in room 3L15 at the Laboratoire de Mathématiques d’Orsay; it lasts one hour plus questions. Everyone is welcome, even if you have not attended previously.
To be kept informed about seminar, and perhaps other K-theory/motivic events, sign up to the mailing list here.
| Date | Speaker & title |
| The seminar returns in Autumn 2025. |
| Date | Speaker & title |
| 16 June 2025 (double seminar) |
Elden Elmanto (Toronto), 2-3pm Steenrod operations in characteristic p I will explain the construction of Steenrod operations on the mod-p motivic cohomology of characteristic p > 0 schemes. At all primes p, it looks like the motivic Steenrod algebra at odd primes modulo the infamous element called tau but with all the expected properties. I will discuss one (or two, or three) of the following applications: 1. a non-smoothable cycle on a smooth, projective F_p-scheme; 2. a cycle on a singular scheme that isn't liftable to bordism class; 3. the integral crystalline Tate condition and its connections to Kato-Saito class field theory. This is joint work with Toni Annala. Rok Gregoric (Johns Hopkins), 3.30-4.30pm Even periodization of spectral stacks A ring spectrum is called "even periodic" if its odd homotopy groups vanish and the even ones are all isomorphic. This condition has long been imposed in certain contexts in homotopy theory for the technical simplifications it brings, but the recent work of Hahn-Raksit-Wilson on the even filtration has led us to revisit it as a more fundamental notion. As such, we introduce even periodization: an operation which approximates a spectral stack as closely as possible by affines corresponding to even periodic ring spectra. In this talk, we will discuss how this recovers and geometrizes the even filtration of Hahn-Raksit-Wilson, and how it gives rise to canonical spectral enhancements of (versions of) the prismatization stacks of Bhatt-Lurie and Drinfeld, extending the approach to prismatic cohomology via topological Hochschild homology of Bhatt-Morrow-Scholze. |
| 2 June 2025 | Maxime Ramzi (Münster) Motives as a localization of categories The category of localizing motives introduced by Blumberg-Gepner-Tabuada serves as a natural place for studying "noncommutative" cohomological invariants such as K-theory, (topological) Hochschild homology, Weibel's homotopy K-theory, etc. Much about these invariants can be encoded in this category. The goal of this talk will be to present joint work with Vova Sosnilo and Christoph Winges in which we show that the universal localizing invariant of stable oo-categories Cat^st -> Mot_loc is a Dwyer-Kan localization at a certain class of "motivic equivalences", thereby generalizing the universal property and usefulness of the category Mot_loc. Time permitting, I will discuss some applications of this result to results of "multiplicative" type. |
| 19 May 2025 | Hyungseop Kim (Orsay) Some formal gluing diagrams for continuous K-theory The study of descent properties of K-theory plays an important role in understanding its values and behaviour in many geometric contexts. In this talk, I will explain a construction of certain diagrams arising from formal gluing situations for which continuous K-theory, and more generally all localising invariants, satisfy descent, from the perspective of dualisable categories. I will also discuss how this encompasses both Clausen–Scholze’s gluing result for analytic adic spaces and an adelic descent result for dualisable categories. |
| 5 May 2025 | Maria Yakerson (CNRS & IMJ-PRG) Fun facts about p-perfection In this talk we will discuss the structure of E_oo-monoids on which a prime p acts invertibly, which we call p-perfect. In particular, we prove that in many examples, they almost embed in their group-completion. We further study the p-perfection functor, and describe it in terms of Quillen's +-construction, similarly to group completion. This is joint work with Maxime Ramzi. |
| Thursday 14 November 2024 | Marc Hoyis (Regensburg) Grothendieck-Witt theory of derived schemes It is an insight of Jacob Lurie that the input to Grothendieck-Witt theory is a stable category with a non-degenerate quadratic functor. Defining the GW-theory of schemes therefore means choosing a quadratic functor on the category of perfect quasi-coherent sheaves. For derived schemes, there is a particularly canonical family of choices, whose resulting GW-theories satisfy Nisnevich descent and a projective bundle formula, and assemble into a (non-A^1-invariant) motivc spectrum KO. This is based on work in progress with Markus Land and Wolfgang Steimle. |
| Wednesday 25 September 2024 | Georg Tamme (Mainz) Pro-cdh descent on derived schemes |