Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis

ISBN-13: 9780521470605 / Angielski / Twarda / 1995 / 360 str.

G. Laumon; Gerard Laumon; Girard Laumon

Opis

Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.

Recenzje

Review of the hardback: 'This is a very impressive achievement.' H.J. Baues, Mathematika

Spis treści

1. Construction of Drinfeld modular varieties; 2. Drinfeld A-modules; 3. The Lefschetz numbers of Hecke operators; 4. The fundamental lemma; 5. Very cuspidal Euler–Poincaré functions; 6. The Lefschetz numbers as sums of global elliptic orbital integrals; 7. Unramified principal series representations; 8. Euler-Poincaré functions as pseudocoefficients of the Steinberg relation; Appendices.