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• W2912076476 abstract "Abstract Let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>X</m:mi> <m:mo>/</m:mo> <m:mi>s</m:mi> </m:mrow> </m:math> {X/s} be a proper log smooth scheme of Cartier type over a fine log scheme whose underlying scheme is the spectrum of a perfect field κ of characteristic <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>p</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {p>0} . In this article we prove that the cohomology of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi mathvariant=script>𝒲</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:msub> <m:mi mathvariant=script>𝒪</m:mi> <m:mi>X</m:mi> </m:msub> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {{mathcal{W}}({mathcal{O}}_{X})} is a finitely generated <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi mathvariant=script>𝒲</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>κ</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {{mathcal{W}}(kappa)} -module if the Yobuko height of X is finite. As an application of this result, we prove that, if the Yobuko height of a proper smooth threefold Y over κ is finite, then the crystalline cohomology of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>Y</m:mi> <m:mo>/</m:mo> <m:mi>κ</m:mi> </m:mrow> </m:math> {Y/kappa} has the Hodge–Witt decomposition and the p -primary torsion part of the Chow group of codimension 2 of Y is of finite cotype. These are nontrivial generalizations of results in [K. Joshi and C. S. Rajan, Frobenius splitting and ordinarity, Int. Math. Res. Not. IMRN 2003 2003, 2, 109–121] and [K. Joshi, Exotic torsion, Frobenius splitting and the slope spectral sequence, Canad. Math. Bull. 50 2007, 4, 567–578]. We also prove a fundamental inequality between the Artin–Mazur heights and the Yobuko height of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>X</m:mi> <m:mo>/</m:mo> <m:mi>s</m:mi> </m:mrow> </m:math> {X/s} if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>X</m:mi> <m:mo>/</m:mo> <m:mi>s</m:mi> </m:mrow> </m:math> {X/s} satisfies natural conditions." @default.
• W2912076476 created "2019-02-21" @default.
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• W2912076476 date "2022-04-20" @default.
• W2912076476 modified "2023-09-26" @default.
• W2912076476 title "Artin–Mazur heights and Yobuko heights of proper log smooth schemes of Cartier type, and Hodge–Witt decompositions and Chow groups of quasi-<i>F</i>-split threefolds" @default.
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