5 papers
Arithmetic Hirzebruch Zagier cycles
S. Kudla, M. Rapoport
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 c…
Height pairings on Shimura curves and p-adic uniformization
S. Kudla, M. Rapoport
We establish a relation between intersection numbers of special cycles on a Shimura curve and special values of derivatives of metaplectic Eisenstein series at a place of bad reduc…
A peculiar modular form of weight one
Stephen S. Kudla, Michael Rapoport, Tonghai Yang
In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious p…
Cycles on Siegel 3-folds and derivatives of Eisenstein series
S. Kudla, M. Rapoport
We consider the Siegel modular variety of genus 2 and a p-integral model of it for a good prime p>2, which parametrizes principally polarized abelian varieties of dimension two wit…
A geometric approach to the fundamental lemma for unitary groups
G. Laumon, M. Rapoport
We consider from a geometric point of view the conjectural fundamental lemma of Langlands and Shelstad for unitary groups over a local field of positive characteristic. We introduc…