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Explicit Hecke descent for special cycles

Syed Waqar Ali Shah
Vol. 20 (2026), No. 8, 1649–1676
DOI: 10.2140/ant.2026.20.1649
Abstract

We derive an explicit formula for the action of a geometric Hecke correspondence on special cycles on a Shimura variety in terms of such cycles at a fixed neat level and compare it with another closely related expression that is valid for modular curves. We provide evidence that the two formulas do not agree in general.

Keywords
special cycles, Hecke correspondences, Shimura varieties, descent
Mathematical Subject Classification
Primary: 11G18, 14C25, 14G35
Milestones
Received: 22 October 2024
Revised: 5 April 2025
Accepted: 27 June 2025
Published: 25 September 2026
Authors
Syed Waqar Ali Shah
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA
United States		 Department of Mathematics
Bilkent University
Ankara
Turkey
© 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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