English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this article we prove a fundamental inequality between Artin-Mazur heightsand Yobuko heights of certain proper log smooth schemes of Cartier type over afine log scheme whose underlying scheme is the spectrum of a perfect field$\kappa$ of characteristic $p>0$. We also prove that the cohomologies ofWitt-sheaves of them are finitely generated ${\cal W}(\kappa)$-modules if theYobuko heights of them are finite. As an application, we prove that the$p$-primary torsion parts of the Chow groups of codimension $2$ of propersmooth threefolds over $\kappa$ is of finite cotype if the Yobuko heights ofthem are finite. These are nontrivial generalizations of results in [JR] and[J].

Artin-Mazur heights and Yobuko heights of proper log smooth schemes of  Cartier type, and Hodge-Witt decompositions and Chow groups of  quasi-$F$-split threefolds