Includes bibliographical references (p. 147-155) and indexes.
Contents:
ch. 1. Introduction
ch. 2. Examples
ch. 3. The Chebotarev density theorem for a number field
ch. 4. Review of -adic cohomology
ch. 5. Auxiliary results on group representations
ch. 6. The -adic properties of N_X(p)
ch. 7. The archimedean properties of N_X(p)
ch. 8. The Sato-Tate conjecture
ch. 9. Higher dimension : the prime number theorem and the Chebotarev theorem.
Summary:
"This book presents several basic techniques in algebraic geometry, group representations, number theory, -adic and standard cohomology, and modular forms. It explores how NX(p) varies with p when the family (X) of polynomial equations is fixed. The text examines the size and congruence properties of NX(p) and describes the ways in which it is computed. Along with covering open problems and offering simple, illustrative examples, the author presents various theorems, including the Chebotarev density theorem and the prime number theorem"-- Provided by publisher.
"The main topic involves counting solutions mod p of a system of polynomial equations, as p varies. The book is based on a series of lectures presented by the author in Taiwan. Using this idea, Serre visits algebra and number theory and asks some non-standard questions, especially on group representations"-- Provided by publisher.