Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series

  • Jan Hendrik Bruinier

    Technische Universität Darmstadt, Germany
  • Tonghai Yang

    University of Wisconsin, Madison, USA
Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series cover
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Abstract

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. 1613–1674

DOI 10.4171/JEMS/1040