Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groups
Abstract
Let
k
be an algebraically closed field of characteristic
p>0
. Let
D
be a
p
-divisible group over
k
which is not isoclinic. Let $\scrD$ (resp. $\scrD_k$) be the formal deformation space of
D
over $\Spf(W(k))$ (resp. over $\Spf(k)$). We use axioms to construct formal subschemes $\scrG_k$ of $\scrD_k$ that: (i) have canonical structures of formal Lie groups over $\Spf(k)$ associated to
p
-divisible groups over
k
, and (ii) give birth, via all geometric points $\Spf(K)\to\scrG_k$, to
p
-divisible groups over
K
that are isomorphic to
D
K
. We also identify when there exist formal subschemes $\scrG$ of $\scrD$ which lift $\scrG_k$ and which have natural structures of formal Lie groups over $\Spf(W(k))$ associated to
p
-divisible groups over
W(k)
. Applications to Traverso (ultimate) stratifications are included as well.