Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties
By Torsten Ekedahl, Gerard van der Geer. 2004
83 citations recorded by the source corpus.
We introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarized abelian variety in positive characteristic. We study its geometric properties, such as irreducibility of the strata, and we calculate the cycle classes. When the characteristic p is treated as a formal variable these classes can be seen as a deformation of the classes of the Schubert varieties for the corresponding classical flag variety (the classical case is recovered by putting p equal to 0). We relate our stratification with the E-O stratification on the moduli space of principally polarized abelian varieties of a fixed dimension and derive properties of the latter. Our results are strongly linked with the combinatorics of the Weyl group of the symplectic group.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/205978c8ab0eeb71210aecf8e78d83977cc71923
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “The Op-scheme F l K is a simultaneous generalization of aspects of work of Griffiths-Schmid over C [44] (see also the works Carayol cited in the introduction) and work of Ekedahl-van der Geer [28] in characteristic p > 0.”
- Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, background): “The works of van der Geer [15] and Ekedahl-van der Geer [11] are also closely related to [39].”