Steve Kudla, University of Toronto
Title: On the subring of special cycle classes for certain orthogonal Shimura varieties
Abstract: Suppose that V is a quadratic space over a totally real field F of degree d such that V has signature (m,2) at d_+ archimedean places and signature (m+2,0) at the remaining d-d_+ such places. Assume that d_+>0 and that V is anisotropic. Special cycles in the corresponding Shimura variety Sh(V) occur in codimensions n d_+, with n between 1 and m. Their cohomology classes generate a subring of the cohomology of Sh(V).
We consider the ring obtained by taking the quotient of this natural special cycle ring by the radical of the restriction of the intersection product. The structure of the resulting subring of special cycles can be given an explicit description in terms of the Fourier coefficients of Hilbert-Siegel Eisenstein series. As a consequence, one obtains isometric isomorphism between certain of these rings for different spaces V. Finally, there is a curious combinatorial construction of a 'subring of special cycles' in the case d_+=0.
听