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arXiv · 2106.14329

Global generation of test ideals in mixed characteristic and applications

Christopher Hacon·Alicia Lamarche·Karl Schwede
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Abstract

Suppose that $X$ is an integral scheme (quasi-)projective over a complete local ring of mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a notion of a $+$-test ideal on $X$, including for divisors and linear series. We obtain global generation results in this setting that generalize the well known global generation results obtained via multiplier ideal sheaf techniques in characteristic $0$ and via test ideals in characteristic $p>0$. We also obtain applications to the order of vanishing of linear series and to the diminished base locus in mixed characteristic similar to results of Ein-Lazarsfeld-Mustata-Nakamaye-Popa, Nakayama, and Mustata in the equal characteristic case.

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Christopher Hacon, Alicia Lamarche, Karl Schwede. 2021-06-27. Global generation of test ideals in mixed characteristic and applications. https://arxiv.org/abs/2106.14329

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