Zeta Functions of Picard Modular Surfaces
American Mathematical Society (Verlag)
978-2-921120-08-1 (ISBN)
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Although 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, generically called 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 this volume as Picard modular surfaces. The contributors have provided a coherent and thorough account of necessary ideas and techniques, many of which are novel and not previously published.
Canonical models of Picard modular surfaces; Arithmetic compactification of some Shimura surfaces; 2-cohomology is intersection cohomology; Analytic expression for the number of points mod p; Contribution of the points at the boundary; The points on a Shimura variety modulo a prime of good reduction; The description of the theorem; Orbital integrals of U(3); Remarks on Igusa theory and real orbital integrals; Calculation of some orbital integrals; Fundamental lemmas for U(3) and related groups; The multiplicity formula for A-packets; Tate classes and arithmetic quotients of the two-ball; The Albanese of unitary Shimura varieties; Lefschetz numbers of Hecke correspondences; On the shape of the contribution of a fixed point on the boundary: The case of Q-rank one; Appendix
| Erscheint lt. Verlag | 26.11.1998 |
|---|---|
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 1043 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 2-921120-08-9 / 2921120089 |
| ISBN-13 | 978-2-921120-08-1 / 9782921120081 |
| Zustand | Neuware |
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