eBook ISBN:  9781470417703 
Product Code:  CRMM/11.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
eBook ISBN:  9781470417703 
Product Code:  CRMM/11.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 

Book DetailsCRM Monograph SeriesVolume: 11; 2000; 97 ppMSC: Primary 19; Secondary 14
This book is the longawaited 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 intimatelyconnected new branches of arithmetic algebraic geometry, such as regulators and special values of Lfunctions 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 copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and researchers interested in arithmetic algebraic geometry, algebraic \(K\)theory, and motives.

Table of Contents

Chapters

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


Additional Material

Reviews

The editors were indeed welladvised 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


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This book is the longawaited 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 intimatelyconnected new branches of arithmetic algebraic geometry, such as regulators and special values of Lfunctions 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 copublished with the Centre de recherches mathématiques.
Graduate students and researchers interested in arithmetic algebraic geometry, algebraic \(K\)theory, and motives.

Chapters

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

The editors were indeed welladvised 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