Co-rank 1 Arithmetic Siegel--Weil
Name
chen-rcchen-phd-math-2025-thesis.pdf
Description
Thesis PDF
Size
2.31 MB
Format
Adobe PDF
Checksum (MD5)
9c61dccd6dc795db40433b8a5815d58f
Author(s)
Chen, Ryan C.
Advisor(s)
Zhang, Wei
Date Issued
May 2025
Publisher
Massachusetts Institute of Technology
Abstract
We prove the arithmetic Siegel–Weil formula in co-rank 1, for Kudla–Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even arithmetic dimension. We also propose a construction for arithmetic special cycle classes associated to possibly singular matrices of arbitrary co-rank. Our arithmetic Siegel–Weil formula implies that degrees of Kudla–Rapoport arithmetic special 1-cycles are encoded in near-central first derivatives of unitary Eisenstein series Fourier coefficients. The key input is a new limiting method at all places. On the analytic side, the limit relates local Whittaker functions on different groups. On the geometric side at nonsplit non-Archimedean places, the limit relates degrees of 0-cycles on Rapoport–Zink spaces and local contributions to heights of 1-cycles in mixed characteristic.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
In Copyright - Educational Use Permitted
Copyright retained by author(s)
Persistent DSpace Link
