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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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Cite

BibTeXRIS
BibTeX
@misc{iwane2026nonnef,
  title = {{Non-nef loci in mixed characteristic}},
  author = {Ryotaro Iwane},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02561},
  eprint = {2609.02561},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02561},
}
RIS
TY  - UNPB
TI  - Non-nef loci in mixed characteristic
AU  - Ryotaro Iwane
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02561
UR  - https://arxiv.org/abs/2609.02561
AB  - 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.
ER  -