PM013 492 pages ISBN 2-921120-08-9 1992 |
Robert P. Langlands and Dinakar Ramakrishnan, editorsAlthough they are central objects in the theory of diophantine equations, the zeta-functions of HasseWeil are not well understood. One large class of varieties whose zeta-functions are perhaps within reach are those attached to discrete groups, and called generically Shimura varieties. The techniques involved are difficult: representation theory and harmonic analysis; the trace formula and endoscopy; intersection cohomology and L2-cohomology; and abelian varieties with complex multiplication. The simplest Shimura varieties for which all attendant problems occur are those attached to unitary groups in three variables over imaginary quadratic fields, referred to in the present volume as Picard modular surfaces. In an attempt to render this very new domain accessible to mathematicians in related fields and to students, the contributors have provided a coherent and thorough account of the necessary ideas and techniques, many of them novel and not previously published, and of some applications. Contents
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