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

2024/01/01 by Bhargav Bhatt, Linquan Ma, Bhatt, Bhargav +12 · 4 citations
Computer Science · Mathematics · #13A35 #14F18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2401.00615

openalex publication_date 2024/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• A Criterion for Perfectoid Purity and the Rationality of Thresholds
• Inversion of adjunction for higher rational singularities
• Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings
• On complete integral closedness of the p-adic completion of absolute integral closure

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