ABSTRACT

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in

chapter 1|6 pages

Introduction

chapter 2|8 pages

Examples

chapter 4|14 pages

Review of `-adic cohomology

chapter 5|20 pages

Auxiliary results on group representations

chapter 6|18 pages

The `-adic properties of NX(p)

chapter 7|18 pages

The archimedean properties of NX(p)

chapter 8|30 pages

The Sato-Tate conjecture