ICTS:31882

Video URL

Special cycles on moduli spaces of unitary shtukas, and higher derivatives of L-functions-II (Onlin…

Special cycles on moduli spaces of unitary shtukas, and higher derivatives of L-functions-II (Online)

(2025). Special cycles on moduli spaces of unitary shtukas, and higher derivatives of L-functions-II (Online). SciVideos. https://youtube.com/live/i75trCjdyWA

Special cycles on moduli spaces of unitary shtukas, and higher derivatives of L-functions-II (Online). SciVideos, May. 20, 2025, https://youtube.com/live/i75trCjdyWA 

          @misc{ scivideos_ICTS:31882,
            doi = {},
            url = {https://youtube.com/live/i75trCjdyWA},
            author = {},
            keywords = {},
            language = {en},
            title = {Special cycles on moduli spaces of unitary shtukas, and higher derivatives of L-functions-II (Online)},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31882 see, \url{https://scivideos.org/icts-tifr/31882}}
          }
Benjamin Howard
Talk numberICTS:31882
Source RepositoryICTS-TIFR

Abstract

The arithmetic Siegel-Weil formula, conjectured by Kudla-Rapoport and proved by Li-Zhang, expresses the degrees of certain 0-cycles on integral models of unitary Shimura varieties in terms of the nondegenerate Fourier coefficients of the central derivative of an Eisenstein series.
Feng-Yun-Zhang proved a higher derivative version of this arithmetic Siegel-Weil formula in the function field setting, now expressing degrees of 0-cycles on moduli spaces of unitary shtukas to the nondegenerate Fourier coefficients of higher central derivatives of an Eisenstein series.
The goal of my lecture series is (1) to explain all of this background, (2) extend the results of Feng-Yun-Zhang to include some degenerate coefficients, and (3) deduce from this extension an arithmetic application: the nonvanishing of higher central derivatives of certain Langlands L-functions implies the nonvanishing of classes in the Chow groups of moduli spaces of shtukas.
All of the new results are joint work with Tony Feng and Mikayel Mkrtchyan.