This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students and researchers interested in arithmetic algebraic geometry, algebraic \(K\)-theory, and motives.

Reviews

"The editors were indeed well-advised to publish these lecture notes ... They remain one of the best introductions to the study of special values of \(L\)-functions in arithmetic geometry ... should be (at least) in every library of every department interested in modern number theory."

-- Zentralblatt MATH

Table of Contents

• Introduction
• Tamagawa numbers
• Tamagawa numbers. Continued
• Continuous cohomology
• A theorem of Borel and its reformulation
• The regulator map. I
• The dilogarithm function
• The regulator map. II
• The regulator map and elliptic curves. I
• The regulator map and elliptic curves. II
• Elements in \(K_2(E)\) of an elliptic curve \(E\)
• A regulator formula
• Bibliography
• Index