Conceptual

Cohomological Description of Kato's Ramification Filtration via de Rham-Witt Sheaves

Give a cohomological description of Kato's ramification filtration on the Galois cohomology of a Henselian discrete-valued field of characteristic p, and of its scheme-theoretic analogue on the cohomology of the complement of a simple normal crossing divisor, in terms of de Rham-Witt sheaves. Develop the filtered de Rham-Witt complex of F-finite regular schemes in characteristic p and apply it to prove a refined Jannsen-Saito-Zhao duality and a Lefschetz theorem for the ramified Brauer group with modulus.