PreprintCC BY 4.0arXiv
Spreading out perverse sheaves
Abstract
We spread out geometrically irreducible perverse sheaves. Over an arithmetic base scheme, such sheaves extend from the generic fiber to a relatively perverse, universally locally acyclic sheaf over a dense open of the base scheme. As an application, we prove the arithmetic Kashiwara conjecture by Esnault and Kerz for geometric traits in equicharacteristic and generalize the decomposition theorem for arithmetic complexes to fields finitely generated over a separably closed field. We also recover the Hard Lefschetz theorem for arithmetic perverse sheaves.
Related
BibTeX
@misc{zurbuchen2026spreading,
title = {{Spreading out perverse sheaves}},
author = {Beat Zurbuchen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06707},
eprint = {2610.06707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06707},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spreading out perverse sheaves
AU - Beat Zurbuchen
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06707
UR - https://arxiv.org/abs/2610.06707
AB - We spread out geometrically irreducible perverse sheaves. Over an arithmetic base scheme, such sheaves extend from the generic fiber to a relatively perverse, universally locally acyclic sheaf over a dense open of the base scheme. As an application, we prove the arithmetic Kashiwara conjecture by Esnault and Kerz for geometric traits in equicharacteristic and generalize the decomposition theorem for arithmetic complexes to fields finitely generated over a separably closed field. We also recover the Hard Lefschetz theorem for arithmetic perverse sheaves.
ER -