CONGRUENCE RELATIONS FOR SHIMURA VARIETIES ASSOCIATED TO SOME UNITARY GROUPS

By O. Bueltel, T. Wedhorn. Journal of the Institute of Mathematics of Jussieu, 2002

54 citations recorded by the source corpus.

In this paper we study the reduction to characteristic $p$ of the Shimura variety associated to a unitary group which has signature $(n-1,1)$ at its real place. We describe the Newton polygon, the Ekedahl–Oort, and the final stratification. In addition we examine the moduli space of $p$-isogenies using a variant of the local model for Shimura varieties. We apply our results to obtain a proof of the Eichler–Shimura congruence relation for the case that $n$ is even.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/06b860a1565edfc3501e05cc552bf6b9ca1033b6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. T. Wedhorn
2. E. Viehmann
3. Inken Vollaard
4. Xuhua He
5. Michael Rapoport
6. Chao Zhang
7. E. Lau
8. S. Kudla

In Mathematical Physics

1. T. Wedhorn
2. E. Viehmann
3. Inken Vollaard
4. Xuhua He
5. Michael Rapoport
6. Chao Zhang
7. E. Lau
8. S. Kudla

In Statistical and Nonlinear Physics

1. Inken Vollaard
2. E. Viehmann
3. T. Wedhorn

Citations in the corpus

• The Supersingular Locus of the Shimura Variety for GU(1, s) (2005, background): “losed subscheme of MF which is proper over SpecF. Our goal is to describe the irreducible components of Mssand their intersection behaviour. The supersingular locus Mss contains an Fp-rational point ([BW] Lem. 5.2). We will view Mssas a scheme over Fp. Let x= (A⊗Z Z (p),ι⊗Z Z (p),λ,η) ∈ Mss(Fp) and ”
• Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, background): “the derived group of GR is isomorphic to SU(1,n− 1), and the prime pis chosen such that only the case (AU) in the classification in Remark 1.3 occurs) has been studied by Bültel and the second author ([BW], see also [VW]). In this case W= Sn, J= {τ2,...,τn−1} (where τi denotes the transposition of ia”