Vol. 14, No. 10, 2020

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Relative crystalline representations and $p$-divisible groups in the small ramification case

Tong Liu and Yong Suk Moon

Vol. 14 (2020), No. 10, 2773–2789
Abstract

Let k be a perfect field of characteristic p > 2, and let K be a finite totally ramified extension over W(k)[1 p] of ramification degree e. Let R0 be a relative base ring over W(k)t1±1,,tm±1 satisfying some mild conditions, and let R = R0 W(k)𝒪K. We show that if e < p 1, then every crystalline representation of π1e ́ t(SpecR[1 p]) with Hodge–Tate weights in [0,1] arises from a p-divisible group over R.

Keywords
crystalline representation, $p$-divisible group, relative $p$-adic Hodge theory
Mathematical Subject Classification 2010
Primary: 11F80
Secondary: 11S20, 14L05
Milestones
Received: 2 October 2019
Revised: 14 May 2020
Accepted: 24 June 2020
Published: 19 November 2020
Authors
Tong Liu
Purdue University
West Lafayette, IN
United States
Yong Suk Moon
University of Arizona
Tucson, AZ
United States