Research Papers
Integral motives and Artin perverse sheaves: t-structures and Lefschetz properties
In my Ph. D. thesis, I study the motivic t-structure on the category of Artin motives and the perverse t-structure on Artin ℓ-adic complexes. The thesis is made of 3 parts: the first one (in french) contains reminders on the thory of stable monoidal ∞-categories, on the 6 functors formalism and about étale motives and Bhatt-Scholze's ℓ-adic complexes. The other parts are my papers Artin Perverse sheaves and Abelian categories of Artin motives with integral coefficients.
Abelian categories of Artin Motives with integral coefficients
Preprint: https://arxiv.org/abs/2211.02505 ([math.AG], 2022, 121 pages).
In this paper, I study the motivic t-structure on the category of Artin motives. This study involves an analogue of the Affine Lefschetz Theorem and a study of Ayoub and Zucker's Artin truncation functor with integral coefficients. One of the main problems is that torsion Artin motives identify with torsion étale sheaves and can therefore have pathological behaviors.
Artin Perverse Sheaves
Preprint: https://arxiv.org/abs/2205.07796 ([math.AG], 2022, 64 pages).
In this paper, I study how the perverse t-sturcture behaves with 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.