English

Canonical subgroups via Breuil-Kisin modules

Number Theory 2012-11-27 v5

Abstract

Let p>2 be a rational prime and K/Q_p be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over O_K with 0<d<h. In this paper, we show that an upper ramification subgroup G^j+ is free of rank d over Z/p^nZ if the Hasse invariant of G is less than 1/(2p^(n-1)). We also prove the usual properties as the canonical subgroup.

Cite

@article{arxiv.1012.1110,
  title  = {Canonical subgroups via Breuil-Kisin modules},
  author = {Shin Hattori},
  journal= {arXiv preprint arXiv:1012.1110},
  year   = {2012}
}

Comments

24 pages; refereed version; results improved; The final publication is available at springerlink.com, http://link.springer.com/article/10.1007%2Fs00209-012-1102-0

R2 v1 2026-06-21T16:53:55.419Z