Moduli of p-divisible groups

Peter Scholze; Jared Weinstein

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arXiv · 1211.6357

Moduli of p-divisible groups

Peter Scholze·Jared Weinstein

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Abstract

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of p-adic Hodge theory. This allows us to formulate and prove duality isomorphisms between basic Rapoport-Zink spaces at infinite level in general. Moreover, we identify the image of the period morphism, reproving results of Faltings. For this, we give a general classification of p-divisible groups over the ring of integers of a complete algebraically closed field in the spirit of Riemann's classification of complex abelian varieties. Another key ingredient is a full faithfulness result for the Dieudonné module functor for p-divisible groups over semiperfect rings (meaning rings on which the Frobenius map is surjective).

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Peter Scholze, Jared Weinstein. 2013-04-13. Moduli of p-divisible groups. https://arxiv.org/abs/1211.6357

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