Eichler-Shimura Relations for Shimura Varieties of Hodge Type

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.

Major revision to correct error in previous version; main theorem weakened

References in corpus (3)

• Cycles on Shimura varieties via geometric Satake
• Filtered F-crystals on Shimura varieties of abelian type
• Théorie de la réduction pour les groupes p-divisibles

Cited by in corpus (1)

• Special cycles on orthogonal Shimura varieties