The relative BreuilKisin classification of pdivisible 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 padically complete discrete
valuation ring with perfect residue field. Then Kisin proved that
pdivisible groups over O_K can be classified by some concrete semilinear
algebra object, which are often called Kisin modules (or sometimes,
BreuilKisin modules; or even, Breuil modules).
In this talk, we generalise this result to pdivisible groups over an affine
formal base which is formally smooth over some padic 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 (Zplattice) Galois
representations, including the relative version of Faltings’ integral
comparison theorem for pdivisible groups.
This talk is part of the Number Theory Seminar series.
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