牛顿多边形层的分层与p-可除群的Traverso图
Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups
摘要：
同构数（Isomorphism Number）代数闭域上的p-可除群D的同构截止（isomorphic cutoff）是最小正整数m，使得D[p^m]确定D直到同构（分别为直到Islam）。证明了这些不变量在常数牛顿多边形的p-可除群族中是下连续的。因此，它们允许牛顿多边形地层的细化。在p-可除群的每个同构类中，我们确定了同构截断的最大值，并给出了同构数的一个上界，证明了它在等倾情形下是最优的.特别是，后者反驳了一个猜想的Traverso。作为应用，我们回答了Zink关于D[p^m]的自同态到D的可升性的一个问题.
英文摘要：
The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field is the least positive integer m such that D[p^m] determines D up to isomorphism (resp. up to isogeny). We show that these invariants are lower semicontinuous in families of p-divisible groups of constant Newton polygon. Thus they allow refinements of Newton polygon strata. In each isogeny class of p-divisible groups, we determine the maximal value of isogeny cutoffs and give an upper bound for isomorphism numbers, which is shown to be optimal in the isoclinic case. In particular, the latter disproves a conjecture of Traverso. As an application, we answer a question of Zink on the liftability of an endomorphism of D[p^m] to D.
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