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 Hasse–Weil 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 ## Contents- R. P. Langlands and D. Ramakrishnan,
*Foreword* - B. Gordon,
*Canonical models of Picard modular surfaces* - M. J. Larsen,
*Arithmetic compactification of some Shimura surfaces* - M. Goresky,
`L`^{2}*cohomology is intersection cohomology* - J. Rogawski,
*Analytic expression for the number of points mod p* - R. E. Kottwitz and M. Rapoport,
*Contribution of the points at the boundary* - J. S. Milne,
*The points on a Shimura variety modulo a prime of good reduction* - R. P. Langlands and D. Ramakrishnan,
*The description of the theorem* - T. C. Hales,
*Orbital integrals on*U(3) - R. P. Langlands,
*Remarks on Igusa theory and real orbital integrals* - R. E. Kottwitz,
*Calculation of some orbital integrals* - D. Blasius and J. Rogawski,
*Fundamental lemmas for*U(3)*and related groups* - J. Rogawski,
*The multiplicity formula for A-packets* - D. Blasius and J. Rogawski,
*Tate classes and arithmetic quotients of the two-ball* - V. K. Murty and D. Ramakrishnan,
*The Albanese of unitary Shimura varieties* - M. Goresky and R. MacPherson,
*Lefschetz numbers of Hecke correspondences* - M. Rapoport,
*On the shape of the contribution of a fixed point on the boundary: The case of Q-rank one*
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