Moduli of p-divisible groups

By Peter Scholze, Jared Weinstein. 2012

210 citations recorded by the source corpus.

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 Dieudonn\'e module functor for p-divisible groups over semiperfect rings (meaning rings on which the Frobenius map is surjective).

View Paper: https://www.semanticscholar.org/paper/cf15efd651310a11d6e472a647e925741fc0a3a3

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Citations in the corpus

Towards a theory of local Shimura varieties (2014, unknown): “The imprecision here lies in the term “in the limit”; however, as in [87], the theory of perfectoid spaces should enable one to make sense of it.”
Geometrization of the local Langlands correspondence: an overview (2016, methodology): “Nevertheless we have the following ([10]) that we won’t use later (although this is used by Scholze and Weinstein in [30] that we will use.”
On torsion in the cohomology of locally symmetric varieties (2013, background): “Note that a result very similar in spirit was proved in joint work with Jared Weinstein, [56], for Rapoport-Zink spaces.”
Relative P-adic Hodge Theory: Foundations (2013, methodology): “In case (a), we say that A is preperfectoid ; this definition and some examples are due to Scholze and Weinstein [115].”
On the p-adic cohomology of the Lubin-Tate tower (2015, background): “Moreover, denote byMLT,∞ over F̆ (which lives over the completion of the maximal abelian extension of F , which is a perfectoid field) the perfectoid space constructed in [31], so that MLT,∞ ∼ lim ←− K MLT,K .”