English

Finite group schemes of essential dimension one

Algebraic Geometry 2019-08-23 v2

Abstract

We prove that if a finite group scheme GG over a field kk has essential dimension one, then it embeds in PGL2/kPGL_{2/k}. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any field and a characterisation of all finite group schemes of essential dimension one over algebraically closed fields.

Keywords

Cite

@article{arxiv.1908.02438,
  title  = {Finite group schemes of essential dimension one},
  author = {Najmuddin Fakhruddin},
  journal= {arXiv preprint arXiv:1908.02438},
  year   = {2019}
}

Comments

Corrected an error in the proof of the main theorem that was pointed out by D. Tossici. The results are unchanged

R2 v1 2026-06-23T10:41:41.063Z