2023/03/28 by Frédéric Déglise, Déglise, Frédéric, Niels Feld +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2303.15906
openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we study the functoriality of the coniveau filtration in motivic homotopy theory via a moving lemma over a base scheme, extending previous works of Levine and Bachmann-Yakerson. The main result is that the motivic stable homotopy category can be modeled on a smaller site, the "smooth-smooth site". The proof is based on a new approach to the purity theorem of Morel-Voevodsky using specialization maps, which turns out to hold even in absence of the \mathbbA1-homotopy invariance property. Applications to the homotopy coniveau tower and to higher Chow-Witt groups are given.