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arXiv · 1705.02300

Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers

Linquan Ma·Karl Schwede
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Abstract

Using perfectoid algebras, we introduce a mixed characteristic analog of the multiplier ideal, respectively test ideal, from characteristic zero, respectively $p > 0$, in the case of a regular ambient ring. We prove several properties about this ideal such as subadditivity. We then use these techniques to derive a uniform bound on the growth of symbolic powers of radical ideals in all excellent regular rings. The analogous result was shown in equal characteristic by Ein-Lazarsfeld-Smith and Hochster-Huneke.

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Linquan Ma, Karl Schwede. 2017-05-05. Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers. https://doi.org/10.1007/s00222-018-0813-1

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