Eichler-Shimura Relations for Shimura Varieties of Hodge Type

2020/06/21 by Si Ying Lee, Lee, Si Ying · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2006.11745

Abstract

We show Eicher-Shimura relations for some Shimura varieties of Hodge type, proving a conjecture of Blasius and Rogawski in this case. We show this using a parabolic reduction strategy on the Hecke action on irreducible components of affine Deligne-Lusztig varieties.

Cited by

• Special cycles on orthogonal Shimura varieties

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• Eichler-Shimura relations for local Shimura varieties
• Congruence relations of GSpin Shimura varieties
• The connected components of affine Deligne–Lusztig varieties
• Eichler-Shimura Relation on Intersection Cohomology
• Basic loci in Shimura varieties of Coxeter type