PreprintCC BY 4.0arXiv
Equivariant deformation theory and deformations of homogeneous varieties
Abstract
We show that, in characteristic p, almost all projective homogeneous varieties under a reductive group and with non-reduced stabilizer do not lift to characteristic p2. To this end, first we develop a general framework for equivariant deformation theory, leading to practical criteria ensuring that the deformations of a scheme come with deformations of a group scheme action. Second, we establish a formula to compute the cohomology of equivariant vector bundles over projective homogeneous varieties with non-reduced stabilizer, enabling us to determine the G-module structure of the first cohomology groups of their tangent bundles.
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BibTeX
@misc{sotto2026equivariant,
title = {{Equivariant deformation theory and deformations of homogeneous varieties}},
author = {Noé Sotto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25590},
eprint = {2610.25590},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25590},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Equivariant deformation theory and deformations of homogeneous varieties
AU - Noé Sotto
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25590
UR - https://arxiv.org/abs/2610.25590
AB - We show that, in characteristic p, almost all projective homogeneous varieties under a reductive group and with non-reduced stabilizer do not lift to characteristic p^2. To this end, first we develop a general framework for equivariant deformation theory, leading to practical criteria ensuring that the deformations of a scheme come with deformations of a group scheme action. Second, we establish a formula to compute the cohomology of equivariant vector bundles over projective homogeneous varieties with non-reduced stabilizer, enabling us to determine the G-module structure of the first cohomology groups of their tangent bundles.
ER -