Shou Yoshikawa

Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic

We introduce the notion of Hodge--Tate splitting for schemes in positive characteristic. For a smooth variety $X$ over a perfect field $k$ of characteristic $p>0$, we say that $X$ is Hodge--Tate split if the natural morphism $\mathcal{O}_X \to F_*\Omega^\bullet_{X/k}$ induced by the absolute Frobenius admits a splittin...