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Frobenius liftability of isolated complete intersections
Abstract
We classify Frobenius liftable normal isolated complete intersection singularities of dimension at least three over an algebraically closed field of positive characteristic. In dimension three, they are precisely the regular points and the ordinary double points; in higher dimensions, they are regular. We also characterize Frobenius liftability of the complete local hypersurfaces defined by $xy-g(z,t)$ without assuming that the singularity is isolated. Such a hypersurface is Frobenius liftable if and only if, after a formal change of coordinates, g is a unit times Hpzatb with 0≤ a,b<p.
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BibTeX
@misc{kawakami2026frobenius,
title = {{Frobenius liftability of isolated complete intersections}},
author = {Tatsuro Kawakami and Teppei Takamatsu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18221},
eprint = {2610.18221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18221},
}
RIS
TY - UNPB
TI - Frobenius liftability of isolated complete intersections
AU - Tatsuro Kawakami
AU - Teppei Takamatsu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18221
UR - https://arxiv.org/abs/2610.18221
AB - We classify Frobenius liftable normal isolated complete intersection singularities of dimension at least three over an algebraically closed field of positive characteristic. In dimension three, they are precisely the regular points and the ordinary double points; in higher dimensions, they are regular. We also characterize Frobenius liftability of the complete local hypersurfaces defined by $xy-g(z,t)$ without assuming that the singularity is isolated. Such a hypersurface is Frobenius liftable if and only if, after a formal change of coordinates, g is a unit times H^pz^at^b with 0≤ a,b<p.
ER -