Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series

Mardi 13 novembre 14:15-15:15 - Jan Bruinier - Darmstadt

Résumé : 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 a Siegel Eisenstein series of genus m+1. We report on joint work with Tonghai Yang proving this conjecture for the coefficients of non-singular index T under certain contitions on T. To this end we establish some new local arithmetic Siegel-Weil formulas at the archimedean and non-archimedean places.

Lieu : 3L15 bâtiment 307

Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series  Version PDF