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"Local" finite group schemes and the reduction of abelian varieties

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Mikhail Bondarko
St. Petersburg State University / MPIM
Mit, 2018-08-08 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar
The talk is dedicated to finite flat commutative p-group schemes over
a mixed characteristic complete discrete valuation ring. The relation
of group schemes of this sort to the reduction of abelian varieties
will also be recalled and applied to deduce certain p-adic criteria.
The most difficult result is that the generic fibre functor is "almost
full" on the category of group schemes of the aforementioned type; it
generalizes the fullness theorem of M. Raynaud and improves a theorem
of J. Tate. The main tool is a classification result for local schemes
of this sort (as given by F. Oort and the speaker); it also gives
certain properties of tangent spaces of these schemes.
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