Lefschetz trace formula and l-adic cohomology of Rapoport-Zink tower for GSp(4)
Yoichi Mieda
TL;DR
This paper explores the l-adic cohomology of the GSp(4) Rapoport-Zink tower using the Lefschetz trace formula, revealing connections to the local Jacquet-Langlands correspondence under certain assumptions.
Contribution
It demonstrates the appearance of the local Jacquet-Langlands correspondence in the cohomology of the GSp(4) Rapoport-Zink tower under specific conditions.
Findings
Jacquet-Langlands correspondence appears in cohomology
Lefschetz trace formula applied to Rapoport-Zink tower
Connections between cohomology and automorphic representations
Abstract
We investigate the alternating sum of the l-adic cohomology of the Rapoport-Zink tower for GSp(4) by the Lefschetz trace formula. Under some assumptions on L-packets of GSp(4) and its inner form, we observe that the local Jacquet-Langlands correspondence appears in the cohomology.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Algebraic Geometry and Number Theory