Minimal p-divisible groups

By Frans Oort. 2004

70 citations recorded by the source corpus.

A p-divisible group X can be seen as a tower of building blocks, each of which is isomorphic to the same finite group scheme X[p]. Clearly, if X1 and X2 are isomorphic then X1[p] ∼= X2[p]; however, conversely X1[p] ∼= X2[p] does in general not imply that X1 and X2 are isomorphic. Can we give, over an algebraically closed field in characteristic p, a condition on the p-kernels which ensures this converse? Here are two known examples of such a condition: consider the case that X is ordinary, or the case that X is superspecial (X is the p-divisible group of a product of supersingular elliptic curves); in these cases the p-kernel uniquely determines X.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d8b9c38a036e5318e50baf1785b162489531c0cf

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In Discrete Mathematics and Combinatorics

1. E. Viehmann
2. T. Wedhorn
3. Xuhua He
4. U. Hartl

In Geometry and Topology

1. T. Wedhorn
2. E. Viehmann
3. Xuhua He
4. Chao Zhang
5. E. Lau
6. Michael Rapoport
7. Peter Scholze
8. Ulrich Goertz

In Mathematical Physics

1. T. Wedhorn
2. E. Viehmann
3. Xuhua He
4. Chao Zhang
5. E. Lau
6. Michael Rapoport
7. Peter Scholze
8. Ulrich Goertz

Citations in the corpus

• Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, background): “ see that Oort-minimal p-divisible groups (without any additional structure) are fundamental, and fundamental p-divisible groups are minimal by Remark 8.8. We obtain a new proof of the main result of [Oo4]: Corollary 8.13. Oort-minimal p-divisible groups are minimal in the sense of Definition 8.2. If”
• Foliations in moduli spaces of abelian varieties (2002, unknown): “For a pair (m, n) of coprime non-negative integers we write Hm,n for the p-divisible group as in [7], 5.3; Hm,n can be defined over Fp, it is isogenous with Gm,n and over Fp its endomorphism ring is the maximal order in its endomorphism algebra; these properties characterize Hm,n over an algebraical”
• Truncations of level 1 of elements in the loop group of a reductive group (2009, background): “By definition there is a unique isomorphism class of minimal p - divisible groups in each isogeny class of p -divisible groups (see [Oor05]).”