Special cycles on unitary Shimura curves at ramified primes
Abstract
In this paper, we study special cycles on the Krämer model of $\mathrm{U}(1,1)(F/F_0)$RapoportZink spaces where $F/F_0$ is a ramified quadratic extension of $p$adic number fields with the assumption that the $2$dimensional hermitian space of special quasihomomorphisms is anisotropic. We write down the decomposition of these special cycles and prove a version of KudlaRapoport conjecture in this case. We then apply the local results to compute the intersection numbers of special cycles on unitary Shimura curves and relate these intersection numbers to Fourier coefficients of central derivatives of certain Eisenstein series.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.07158
 Bibcode:
 2020arXiv200407158S
 Keywords:

 Mathematics  Algebraic Geometry;
 11G15
 EPrint:
 arXiv admin note: text overlap with arXiv:0912.3758 by other authors