**CRM Monograph Series**

Volume: 11;
2000;
97 pp;
Softcover

MSC: Primary 19;
Secondary 14

Print ISBN: 978-0-8218-2973-8

Product Code: CRMM/11.S

List Price: $28.00

AMS Member Price: $22.40

MAA Member Price: $25.20

**Electronic ISBN: 978-1-4704-1770-3
Product Code: CRMM/11.E**

List Price: $28.00

AMS Member Price: $22.40

MAA Member Price: $25.20

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# Higher Regulators, Algebraic \(K\)-Theory, and Zeta Functions of Elliptic Curves

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*Spencer J. Bloch*

A co-publication of the AMS and Centre de Recherches Mathématiques

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 & Endorsements

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

# Table of Contents

## Higher Regulators, Algebraic $K$-Theory, and Zeta Functions of Elliptic Curves

- Cover Cover11
- Other titles in this series i2
- Title page iii4
- Author’s apology v6
- Contents vii8
- Acknowledgments ix10
- Introduction 112
- Tamagawa numbers 920
- Tamagawa numbers. Continued 1526
- Continuous cohomology 2334
- A theorem of Borel and its reformulation 2940
- The regulator map. I 3546
- The dilogarithm function 4354
- The regulator map. II 5162
- The regulator map and elliptic curves. I 6172
- The regulator map and elliptic curves. II 6980
- Elements in 𝐾₂(𝐸) of an elliptic curve 𝐸 7586
- A regulator formula 8798
- Bibliography 95106
- Index 97108
- Back Cover Back Cover1114