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S. Mohammad Hadi Hedayatzadeh
Exterior Powers of Lubin-Tate Groups
Journal de théorie des nombres de Bordeaux, 27 no. 1 (2015), p. 77-148, doi: 10.5802/jtnb.895
Article PDF | Reviews MR 3346966
Class. Math.: 14L05, 14F30

Résumé - Abstract

Let $ {\mathcal{O}}$ be the ring of integers of a non-Archimedean local field of characteristic zero and $ \pi $ a fixed uniformizer of $ {\mathcal{O}}$. We prove that the exterior powers of a $ \pi $-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 $ \pi $-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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