TL;DR
This paper establishes a Serre-type duality for Witt-divisorial sheaves of $ ext{Q}$-Cartier divisors on smooth projective varieties over perfect fields of finite characteristic, connecting it to Tanaka's vanishing theorems.
Contribution
It adapts Ekedahl's ideas to prove a new duality result for Witt-divisorial sheaves and relates it to existing vanishing theorems in algebraic geometry.
Findings
Proves Serre-type duality for Witt-divisorial sheaves.
Links duality to Tanaka's vanishing theorems.
Provides a new perspective on divisorial sheaves in positive characteristic.
Abstract
We adapt ideas from Ekedahl [Eke84] to prove a Serre-type duality for Witt-divisorial sheaves of -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].
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