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Finite Symplectic Automorphism Groups of K3 Surfaces in Characteristic Seven
Abstract
We classify all finite groups of order divisible by $7$ that admit a faithful symplectic action on a K3 surface over an algebraically closed field of characteristic seven, together with the possible heights and Artin invariants. Combined with the known classification of tame actions, this gives the complete list of finite groups admitting such an action in characteristic seven.
Related
- K3 surfaces with finite automorphism group in positive characteristic
- Finite subgroups of outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields
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- Large automorphism groups compared to the p-rank of algebraic curves in characteristic p
BibTeX
@misc{wang2026finite,
title = {{Finite Symplectic Automorphism Groups of K3 Surfaces in Characteristic Seven}},
author = {Bin Wang and Zhiwei Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25251},
eprint = {2610.25251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25251},
}
RIS
TY - UNPB
TI - Finite Symplectic Automorphism Groups of K3 Surfaces in Characteristic Seven
AU - Bin Wang
AU - Zhiwei Zheng
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25251
UR - https://arxiv.org/abs/2610.25251
AB - We classify all finite groups of order divisible by $7$ that admit a faithful symplectic action on a K3 surface over an algebraically closed field of characteristic seven, together with the possible heights and Artin invariants. Combined with the known classification of tame actions, this gives the complete list of finite groups admitting such an action in characteristic seven.
ER -