Eichler-Shimura relations for local Shimura varieties
Teruhisa Koshikawa
TL;DR
This paper explores the Eichler-Shimura relation within the context of local Shimura varieties, utilizing recent advances by Fargues-Scholze to deepen understanding of their cohomological properties.
Contribution
It establishes multiple forms of the Eichler-Shimura relation for local Shimura varieties' cohomology, building on Fargues-Scholze's foundational work.
Findings
Different forms of the Eichler-Shimura relation are formulated.
The relations are applied to the compactly supported cohomology of local Shimura varieties.
The work enhances the theoretical framework connecting Shimura varieties and automorphic forms.
Abstract
In this note, we discuss several forms of the Eichler-Shimura relation for the compactly supported cohomology of local Shimura varieties, using the work of Fargues-Scholze.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Geometry and complex manifolds