On the cohomology of regular differential forms and dualizing sheaves

Hübl, Reinhold; Sun, Xiaotao

doi:10.1090/S0002-9939-98-04499-2

On the cohomology of regular differential forms and dualizing sheaves
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by Reinhold Hübl and Xiaotao Sun PDF

Proc. Amer. Math. Soc. 126 (1998), 1931-1940 Request permission

Abstract:

If $Y$ is a local Dedekind scheme and $X/Y$ is a projective Cohen–Macaulay variety of relative dimension $1$, then $R^{1} f_{*} \omega ^{1}_{X/Y}$ is torsionfree if and only if $X/Y$ is arithmetically Cohen–Macaulay for a suitable embedding in $\mathbb {P}^{n}_{k}$. If $X$ is regular then $R^{1} f_{*} \omega ^{1}_{X/Y}$ is torsionfree whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.

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