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arXiv · 2609.02561

Non-nef loci in mixed characteristic

Ryotaro Iwane
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Abstract

We introduce relative versions of non-nef loci and restricted base loci, and investigate a relative version of Boucksom--Broustet--Pacienza's conjecture that these two loci coincide. We prove the conjecture holds for normal integral schemes projective and flat over a Dedekind domain of characteristic zero with mild singularities, such as BCM-regularity. This result is a mixed characteristic analogue of results of Cacciola--Di Biagio in characteristic zero and Sato in positive characteristic. To prove this result, we show that BCM-regularity is preserved under perturbations by divisors with small vanishing order.

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Ryotaro Iwane. 2026-09-02. Non-nef loci in mixed characteristic. https://arxiv.org/abs/2609.02561

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