2025/01/01 by Subhadip Majumder, Majumder, Subhadip
Engineering · #11G25 #19F05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2501.00931
openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a Henselian discrete valued field K of characteristic p>0, Kato defined a ramification filtration \\rm filnHq(K,\mathbb Qp/\mathbb Zp(q-1))\n ≥ 0 on Hq(K,\mathbb Qp/\mathbb Zp(q-1)). One can also define a ramification filtration on Hq(U,\mathbb Z/pm(q-1)) using the local Kato-filtration, where U is the complement of a simple normal crossing divisor in a regular scheme X of characteristic p>0. The main objective of this thesis is to provide a cohomological description of these filtrations using de Rham-Witt sheaves and present several applications. To achieve our goal, we study a theory of the filtered de Rham-Witt complex of F-finite regular schemes of characteristic p>0 and prove several properties which are well known for the classical de Rham-Witt complex of regular schemes. As applications, we prove a refined version of Jannsen-Saito-Zhao's duality over finite fields, and a similar duality for smooth projective curves over local fields. As another application, we prove a Lefschetz theorem for unramified and ramified Brauer group (with modulus) of smooth projective F-finite schemes over a field of characteristic p>0. Further applications are given in [49] and [50].