Exterior Powers of Lubin-Tate Groups

Abstract

Let O be the ring of integers of a non-Archimedean local field of characteristic zero and π a fixed uniformizer of O. We prove that the exterior powers of a π-divisible module of dimension at most 1 over a locally Noetherian scheme exist and commute with arbitrary base change. We calculate the height and dimension of the exterior powers in terms of the height of the given π-divisible module. In the case of p-divisible groups, the existence of the exterior powers are proved without any condition on the basis.

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© 2015 Centre de recherches en mathématiques. Manuscript received 31 August 2013, revised 23 June 2014, accepted 17 October 2014.

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