Higher Siegel-Weil formulae over function fields
Name
mkrtchyan-mikayelm-phd-math-2026-thesis.pdf
Description
Thesis PDF
Size
2.13 MB
Format
Adobe PDF
Checksum (MD5)
2519195276c126a87da39f0e9d9154c6
Author(s)
Mkrtchyan, Mikayel
Advisor(s)
Yun, Zhiwei
Yun, Zhiwei
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
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.
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
