Green forms and the arithmetic Siegel-Weil formula
Number Theory
2019-05-01 v1 Algebraic Geometry
Differential Geometry
Abstract
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean heights.
Cite
@article{arxiv.1808.09313,
title = {Green forms and the arithmetic Siegel-Weil formula},
author = {Luis E. Garcia and Siddarth Sankaran},
journal= {arXiv preprint arXiv:1808.09313},
year = {2019}
}