Voevodsky motives and motives with modulus in positive characteristic

2024/01/23 by Keiho Matsumoto, Matsumoto, Keiho
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2401.13119

openalex publication_date 2024/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field of characteristic p>0. In this paper, without assuming resolution of singularities, we prove that the triangulated category of motives with modulus with rational coefficients is equivalent to Voevodsky's triangulated category of motives with rational coefficients \MDM^\eff(k,\Q)≃ \DM^\eff(k,\Q). Equivalently, after tensoring with \Q, the multiplicities of the modulus become invisible in the category of motives with modulus in positive characteristic.

Related

• Motives with modulus
• Levine's motivic comparison theorem revisited
• Smooth blowup square for motives with modulus
• The triangulated category of K-motives DK_(k)
• The Voevodsky motive of a rank one semiabelian variety