Title: Canonical subgroups in p-adic families of abelian varieties

Abstract: Recently there have appeared several works (by Abbes-Mokrane,
Kisin-Lai, Goren-Kassaei, Andreatta-Gasbarri) on higher-dimensional
generalizations of the Lubin-Katz theory of canonical subgroups in p-adic
families of elliptic curves.  These works impose conditions on the
reduction-type of the fibers or on discrete invariants (by working over a
modular variety of some sort).  We use Berkovich's theory of
rigid-analytic spaces and results of Bosch and Lutkebohmert on semistable
reduction over non-archimedean fields to give a theory of canonical
subgroups (at any p-power level) that has several advantages: there is a
simple and intrinsic fibral definition that has no dependence on auxiliary
discrete invariants (such as polarizations, or level structure), it is
applicable to rather arbitrary p-adic families of abelian varieties (there
is no need to be over a modular or Shimura variety), integral structure on
the base of the p-adic family is irrelevant, and existence is governed by
a "Hasse invariant" depending only on the residue characteristic, the
dimension of the abelian variety, and the exponent of the p-power torsion
order for the subgroups under consideration.