DEFORMATION SUBSPACES OF p-DIVISIBLEGROUPS AS FORMAL LIE GROUPS ASSOCIATEDTO 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 D (resp. D_k)bethe formal deformation space of D over Spf(W(k)) (resp. over Spf(k)).We use axioms to construct formal subschemes gckofD_kthat: (i) havecanonical structures of formal Lie groups over Spf(k) associated to p-divisible groups over k, and (ii) give birth, via all geometric pointsSpf(K)→g_k,to p-divisible groups overKthat are isomorphic toD_KWe also identify when there exist formal subschemes g of D which lift g_kand 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.