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In this article we prove a rigidity result for p-divisible formal groups; see Thm. 4.3 for the statement. An important special case is the following. Consider a formal torus T over an algebraically closed field k of characteristic p > 0. Suppose Z ⊆ T is an irreducible closed formal subscheme of T which is stable under the endomorphism [1 + p]T for some n ≥ 2, where [1+ p]T : T → T denotes “multiplication by 1+ p” on the formal torus T . Then 4.3 asserts that Z is a formal subtorus of T .

A Rigidity Result for p-divisible Formal Groups