Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groups

摘要

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $D$ bea $p$-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 allgeometric points $\Spf(K)\to\scrG_k$, to $p$-divisible groups over $K$ that areisomorphic to $D_K$. We also identify when there exist formal subschemes$\scrG$ of $\scrD$ which lift $\scrG_k$ and which have natural structures offormal Lie groups over $\Spf(W(k))$ associated to $p$-divisible groups over$W(k)$. Applications to Traverso (ultimate) stratifications are included aswell.