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Jan 12, 2016 at 16:56 vote accept user84144
Jan 12, 2016 at 15:55 comment added nfdc23 Both $p$-divisible groups and smooth proper formal schemes over the dvr give rise to crystalline representations (and similarly in the deRham case with smooth proper rigid-analytic spaces), so one gets "crystalline periods" for cohomology far beyond algebraic varieties. Your setup "is" an etale $p$-divisible group over the residue field $k$ (uniquely lifting over $O_K$), so its $W(\overline{k})[1/p]$-admissibility is the slope-0 case of the Dieudonne-Manin classification, illuminating the comment in Sam Derbyshire's answer concerning the need use an algebraic closure of the residue field.
Jan 12, 2016 at 15:09 answer added Sam Derbyshire timeline score: 13
Jan 12, 2016 at 11:31 answer added David Loeffler timeline score: 12
Jan 12, 2016 at 5:41 history edited user84144 CC BY-SA 3.0
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Jan 11, 2016 at 22:18 history asked user84144 CC BY-SA 3.0