Pullback formulas for arithmetic cycles on orthogonal Shimura varieties
Number Theory
2025-06-18 v2
Abstract
On an orthogonal Shimura variety, one has a collection of special cycles in the Gillet-Soule 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, for which we construct logarithmic expansions of certain Green currents on the deformation to the normal bundle of the embedding.
Cite
@article{arxiv.2206.11125,
title = {Pullback formulas for arithmetic cycles on orthogonal Shimura varieties},
author = {Benjamin Howard},
journal= {arXiv preprint arXiv:2206.11125},
year = {2025}
}
Comments
57 pages. Final version. To appear in Algebra and Number Theory