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The relative Breuil-Kisin classification of p-divisible groups

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If you have a question about this talk, please contact Tom Fisher.

Let p>2 be a prime, and let O_K be a p-adically complete discrete valuation ring with perfect residue field. Then Kisin proved that p-divisible groups over O_K can be classified by some concrete semi-linear algebra object, which are often called Kisin modules (or sometimes, Breuil-Kisin modules; or even, Breuil modules).

In this talk, we generalise this result to p-divisible groups over an affine formal base which is formally smooth over some p-adic dvr, under some mild finiteness hypothesis on the base—for example, we allow the base to be the completion of an affine smooth scheme over Zp along the special fibre. We also show compatibility of various construction of (Zp-lattice) Galois representations, including the relative version of Faltings’ integral comparison theorem for p-divisible groups.

This talk is part of the Number Theory Seminar series.

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