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

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.

117 pages, major revision, improved results (removed completeness hypothesis from base DVR, better perturbation/test elements), added appendix by Rankeya Datta, other minor changes and typos corrected, comments welcome

Cited by in corpus (1)

• Centers of perfectoid purity