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arXiv · 2401.00615

Test ideals in mixed characteristic: a unified theory up to perturbation

Bhargav Bhatt·Linquan Ma·Zsolt Patakfalvi·Karl Schwede·Kevin Tucker·Joe Waldron·Jakub Witaszek·Rankeya Datta
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Abstract

Let $X$ be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inverting $p$, is computed from a sufficiently large alteration, agrees with previous mixed characteristic BCM test ideals after completing at any point of residue characteristic $p$ (up to small perturbation), and which satisfies the full suite of expected properties of a multiplier or test ideal. This object is obtained via the $p$-adic Riemann-Hilbert functor.

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Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek, Rankeya Datta. 2024-01-01. Test ideals in mixed characteristic: a unified theory up to perturbation. https://arxiv.org/abs/2401.00615

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