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Pullback formulas for arithmetic cycles on orthogonal Shimura varieties

Benjamin Howard
Vol. 19 (2025), No. 8, 1495–1547
DOI: 10.2140/ant.2025.19.1495
Abstract

On an orthogonal Shimura variety, one has a collection of arithmetic special cycles in the Gillet–Soulé arithmetic Chow group. We describe how these cycles behave under pullback to an embedded orthogonal Shimura variety of lower dimension. The bulk of the paper is devoted to cases in which the special cycles intersect the embedded Shimura variety improperly, which requires that we analyze logarithmic expansions of Green currents on the deformation to the normal bundle of the embedding.

Keywords
arithmetic intersection theory, orthogonal Shimura varieties
Mathematical Subject Classification
Primary: 11G18, 14G40
Milestones
Received: 7 June 2023
Revised: 27 May 2024
Accepted: 3 September 2024
Published: 12 June 2025
Authors
Benjamin Howard
Department of Mathematics
Boston College
Chestnut Hill, MA
United States
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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