Arithmetic Hirzebruch Zagier cycles
摘要
We define special cycles on arithmetic models of twisted Hilbert-Blumenthal surfaces at primes of good reduction. These are arithmetic versions of these cycles. In particular, we characterize the non-degenerate intersections and partially determine the generating series formed from the intersection numbers of them relating it to the value at the center of symmetry of the derivative of a certain metaplectic Eisenstein series in 6 variables. These results are analogous to those obtained by us in the case of Siegel threefolds (alg-geom/9711025). We also study the case of degenerate intersections and show that in this case the intersection locus is a configuration of projective lines whose dual graph is described in terms of subcomplexes of the Bruhat-Tits building of PGL(2,F), where F is an unramified quadratic extension of Q_p.
引用
@article{arxiv.math/9904083,
title = {Arithmetic Hirzebruch Zagier cycles},
author = {S. Kudla and M. Rapoport},
journal= {arXiv preprint arXiv:math/9904083},
year = {2007}
}
备注
106 pages