Arkiv för Matematik

Volume 60 (2022)

Number 1

Duality for Witt-divisorial sheaves

Pages: 107 – 124



Niklas Lemcke (Department of Mathematics, School of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan)


We adapt ideas from Ekedahl [Eke84] to prove a Serre-type duality for Witt-divisorial sheaves of $\mathbb{Q}$‑Cartier divisors on a smooth projective variety over a perfect field of finite characteristic. We also explain its relationship to Tanaka’s vanishing theorems [Tan20].


de Rham–Witt complex, Serre duality, Kodaira vanishing theorem, positive characteristic

2010 Mathematics Subject Classification

14F17, 14F30

Received 10 July 2020

Received revised 31 August 2021

Accepted 11 October 2021

Published 16 May 2022