Serre-Tate theory for moduli spaces of PEL type

By B. Moonen. 2002

88 citations recorded by the source corpus.

Abstract We develop a Serre–Tate theory for moduli spaces of PEL type. This leads us to study Barsotti–Tate groups X equipped with an action ι of a Z p -algebra and possibly also a polarization λ. We define a notion of ordinariness for such triples  X =(X,ι,λ) . If we work over k= k and fix suitable discrete invariants, such as the CM-type, we prove that there is a unique ordinary object, up to isomorphism. We introduce a new structure, called a cascade, that generalizes the notion of a biextension, and we show that the formal deformation space of an ordinary triple has a natural cascade structure. In particular, our theory gives rise to canonical liftings of ordinary objects. In the final section of the paper we apply our theory to the study of congruence relations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b4c92a208dd7cb42f351baf3787f1dc7ac8ee65

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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): “) = w. Remark 8.3. If x∈ G(L) is minimal, then σ(x) is also minimal. This shows that if w∈ JWis minimal, then each element in the same Γk-orbit of w(Remark 4.15) is also minimal. Example 8.4. Moonen ([Mo3], Theorem in Section 0.3) has shown that the µ-ordinary Ekedahl-Oort stratum is minimal in the ”