Higher Siegel--Weil formula for unitary groups II: corank one terms

Fuente: arXiv
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Main Authors: Feng, Tony, Howard, Benjamin, Mkrtchyan, Mikayel
Format: Preprint
Published: 2025
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author Feng, Tony
Howard, Benjamin
Mkrtchyan, Mikayel
author_facet Feng, Tony
Howard, Benjamin
Mkrtchyan, Mikayel
contents We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms.
format Preprint
id arxiv_https___arxiv_org_abs_2507_13473
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Higher Siegel--Weil formula for unitary groups II: corank one terms
Feng, Tony
Howard, Benjamin
Mkrtchyan, Mikayel
Number Theory
Algebraic Geometry
Representation Theory
We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms.
title Higher Siegel--Weil formula for unitary groups II: corank one terms
topic Number Theory
Algebraic Geometry
Representation Theory
url https://arxiv.org/abs/2507.13473