Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series

2018/02/26 by Jan Hendrik Bruinier, Bruinier, Jan Hendrik, Tonghai Yang +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1802.09489

Abstract

Let V be a rational quadratic space of signature (m,2). A conjecture of Kudla relates the arithmetic degrees of top degree special cycles on an integral model of a Shimura variety associated with SO(V) to the coefficients of the central derivative of an incoherent Siegel Eisenstein series of genus m+1. We prove this conjecture for the coefficients of non-singular index T when T is not positive definite. We also prove it when T 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 archimedean and non-archimedian places.

Citations

• On two geometric theta lifts

Cited by

• A new converse theorem for Borcherds products
• Kudla--Rapoport cycles and derivatives of local densities

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