Title: Canonical subgroup for p-divisible groups

Abstract: Let R be a discrete valuation ring of mixed characteristic
with a perfect residue field of characteristic p>0, and G be a
p-divisible group over R. In this talk, we are interested in a
conjecture of Lubin on the existence of a canonical subgroup of G
which lifts the kernel of the Frobenius homomorphism of the special
fiber of G. If G is "not too supersingular", a condition expressed in
terms of the p-adic valuation of the determinant of a certain map
attached to G, we claim that a certain degree of Abbes-Saito's
canonical filtration for the kernel of multiplication by p on G gives
the answer. In order to do this, we will introduce the Bloch-Kato
filtration for a finite and flat group scheme over R killed by p, and
give also a description of its Abbes-Saito's filtration in terms of
congruence subgroups.