Conjectures in Arithmetic Algebraic Geometry

Chapter 1 Introduction

Chapter 2 The zero-dimensional case: number fields

Chapter 3 The one-dimensional case: elliptic curves

Chapter 4 The general formalism of L -functions, Deligne cohomology and Poincaré duality theories

Chapter 5 Riemann-Roch, K-theory and motivic cohomology

Chapter 6 Regulators, Deligne’s conjecture and Beilinson’s first conjecture

Chapter 7 Beilinson’s second conjecture

Chapter 8 Arithmetic intersections and Beilinson’s third conjecture

Chapter 9 Absolute Hodge cohomology, Hodge and Tate conjectures and Abel-Jacobi maps

Chapter 11 Examples and Results

Chapter 12 The Bloch-Kato conjecture