Canonical subgroups via Breuil-Kisin modules

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.

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

References in corpus (3)

• Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields
• Higher-level canonical subgroups for p-divisible groups
• Dualité de Cartier et modules de Breuil

Cited by in corpus (2)

• Classicality of overconvergent Hilbert eigenforms: Case of quadratic residue degree
• On lower ramification subgroups and canonical subgroups