2024/03/27 by Fei Ren, Ren, Fei, Kay Rülling +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2403.18763
openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show that these sheaves correspond under Grothendieck duality for coherent sheaves to de Rham-Witt sheaves on X with modulus (X,D), as defined in the theory of cube invariant modulus sheaves with transfers developed by Kahn-Miyazaki-Saito-Yamazaki. From this we deduce refined versions of Ekedahl - and Poincaré duality for crystalline cohomology generalizing results of Mokrane and Nakkajima for reduced D, and a modulus version of Milne-Kato duality for étale motivic cohomology with p-primary torsion coefficients, which refines a result of Jannsen-Saito-Zhao. We furthermore get new integral models for rigid cohomology with compact supports on the complement of D and a modulus version of Milne's perfect Brauer group pairing for smooth projective surfaces over finite fields.