Ebook: Conjectures in arithmetic algebraic geometry: a survey

This work was originally published in 1992. The main purpose of the book is to give an introduction to Beilinson's conjectures. Two chapters on classical number theory and elliptic curves introduce L-functions and regulators. Topics discussed include Fermat's conjecture, Dirichlet and Artin L-functions, L-functions of elliptic curves, the conjectures of Shimura-Taniyama-Weil, and of Birch and Swinnerton-Dyer. Later chapters deal with the general formulation of Beilinson's conjectures, and those of Hodge and Tate in Jannsen's approach. Also, the necessary tools - such as higher algebraic K-theroy, Poincare duality theories, Chern characters and motives - are treated in some detail. In the final chapter, a few examples are discussed of cases where some of the conjectures are verified.