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

2019/02/01 by Nakkajima, Yukiyoshi
#14F30 #14F40 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.00185

Abstract

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

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