Research

Artin Perverse Sheaves, in Journal of algebra, https://doi.org/10.1016/j.jalgebra.2023.10.022. pages 596-677.

In this paper, I study how the perverse t-sturcture behaves with respect to the Artin condition on ℓ-adic complexes. This study involves the proétale topology, Morel's weight truncation and dévissage techniques which only work over small dimensional schemes. When the scheme is 3-dimensional, the perverse t-structure does not respect the Artin condition in general.

Étale motives of geometric origin, https://arxiv.org/abs/2405.07095, 15 pages. To appear in Bulletin of the LMS.

Over qcqs finite-dimensional schemes, we prove that étale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full answer to the question "Do all constructible étale motives come from geometry?" which dates back to Cisinski and Déglise's work. We also show that they afford the continuity property and satisfy h-descent and Milnor excision. 

Integral Artin motives II: Perverse motives and Artin Vanishing Theorem, https://arxiv.org/abs/2504.15732, 77 pages.

In this text, we are mainly interested in the existence of the perverse motivic t-structures on Artin étale motives with integral coefficients. We also construct the perverse homotopy t-structure which is the best possible approximation to a perverse t-structure on Artin motives with rational coefficients. The heart of this t-structure has properties similar to those of the category of perverse sheaves and contains the Ayoub-Zucker motive. 

With integral coefficients, we construct the perverse motivic t-structure on Artin motives when the base scheme is of dimension at most 2 and show that this result falls short in dimension 4. This construction relies notably on a an analogue for Artin motives of the Artin Vanishing Theorem. 

Nori motives (and mixed Hodge modules) with integral coefficients, https://arxiv.org/abs/2407.01462, 66 pages.

We construct abelian categories of integral Nori motivic sheaves over a scheme of characteristic zero. The first step is to study the presentable derived category of Nori motives over a field. Next we construct an algebra in étale motives such that modules over it afford a t-structure that restricts to constructible objects. This category of integral Nori motives has the six operations and arc-descent. We finish by providing analogous constructions and results for mixed Hodge modules on schemes over the reals.

Integral Artin motives I: Smooth objects and the ordinary t-structyre, https://arxiv.org/abs/2211.02505, 46 pages.

We link smooth Artin motives to étale local systems and Artin representations. We then construct the ordinary motivic t-structure on Artin motives with integral coefficients and show that the ℓ-adic realization functor is t-exact.

My thesis consists of my first three papers: Artin perverse sheaves and Integral Artin motives I & II (see above).

Here is a complete version. The interested reader can also find a long and somewhat elementary introduction to motives at the beginning of the thesis.