Higher Siegel-Weil formulae over function fields

In their seminal work, Feng-Yun-Zhang introduced function field analogues of Kudla-Rapoport cycles for moduli spaces of unitary shtukas, and initiated the study of their intersection theory. They proved a higher Siegel-Weil formula in the case of non-degenerate Fourier coefficients, relating the degrees of these cycles to higher derivatives of Siegel-Eisenstein series. In this thesis, we generalize their result in two directions: we 1) prove a higher Siegel-Weil formula for unitary groups for corank-1 degenerate coefficients, and 2) introduce analogous cycles on moduli spaces of symplectic shtukas, and prove a higher Siegel-Weil formula for such cycles in the non-degenerate case, relating their degrees to derivatives of Siegel-Eisenstein series on split orthogonal groups.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2026

Author dc:creator

• Mkrtchyan, Mikayel

Advisor dc:contributor.advisor

• Yun, Zhiwei

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/164977

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/164977