Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
Jan Hendrik BruinierTechnische Universität Darmstadt, Germany
Tonghai YangUniversity of Wisconsin, Madison, USA
Let be a rational quadratic space of signature . A conjecture of Kudla relates the arithmetic degrees of top degree special cycles on an integral model of a Shimura variety associated with to the coefficients of the central derivative of an incoherent Siegel Eisenstein series of genus . We prove this conjecture for the coefficients of non-singular index when is not positive definite. We also prove it when is positive definite and the corresponding special cycle has dimension 0. To obtain these results, we establish new local arithmetic Siegel–Weil formulas at the archimedian and non-archimedian places.
Cite this article
Jan Hendrik Bruinier, Tonghai Yang, Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series. J. Eur. Math. Soc. 23 (2021), no. 5, pp. 1613–1674DOI 10.4171/JEMS/1040