| eBook ISBN: | 978-0-8218-7641-1 |
| Product Code: | CONM/55.1.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-0-8218-7641-1 |
| Product Code: | CONM/55.1.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
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Book DetailsContemporary MathematicsVolume: 55; 1986; 406 ppMSC: Primary 18
This volume presents a state-of-the-art description of some of the exciting applications of algebraic \(K\)-theory to other branches of mathematics, especially algebraic geometry and algebraic number theory. As the proceedings of a 1983 AMS-IMS-SIAM Joint Summer Research Conference, it includes current and important work by some of the best researchers in the field. The diverse scope includes the following topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field to higher \(K\)-groups of varieties over number fields.
Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating \(K\)-theory to the Brauer group (as reported by Merkurjev and Wadsworth), and the papers by Kato on algebraic cycles.
Directed towards mathematicians working in algebraic \(K\)-theory, algebraic geometry, and algebraic number theory, this volume is also of interest to the algebraic topologist. The reader should be familiar with basic \(K\)-theory and interested in its applications to other areas of mathematics.
This item is also available as part of a set: -
Table of Contents
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Articles
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A. A. Beĭlinson — Higher regulators of modular curves [ MR 862627 ]
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A. A. Beĭlinson — Notes on absolute Hodge cohomology [ MR 862628 ]
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A. J. Berrick and M. E. Keating — The $K$-theory of triangular matrix rings [ MR 862629 ]
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S. Bloch — A note on Gersten’s conjecture in the mixed characteristic case [ MR 862630 ]
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S. Bloch and D. Grayson — $K_2$ and $L$-functions of elliptic curves: computer calculations [ MR 862631 ]
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Dan Burghelea — Cyclic homology and the algebraic $K$-theory of spaces. I [ MR 862632 ]
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Kevin R. Coombes — Local class field theory for curves [ MR 862633 ]
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W. G. Dwyer and E. M. Friedlander — Conjectural calculations of general linear group homology [ MR 862634 ]
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William G. Dwyer and Eric M. Friedlander — Some remarks on the $K$-theory of fields [ MR 862635 ]
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Henri Gillet — The $K$-theory of twisted complexes [ MR 862636 ]
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J. F. Jardine — Simplicial objects in a Grothendieck topos [ MR 862637 ]
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Kazuya Kato — Milnor $K$-theory and the Chow group of zero cycles [ MR 862638 ]
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Kazuya Kato and Shuji Saito — Global class field theory of arithmetic schemes [ MR 862639 ]
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Aderemi O. Kuku — $K_n,\;SK_n$ of integral group-rings and orders [ MR 862640 ]
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Claudio Pedrini and Charles A. Weibel — $K$-theory and Chow groups on singular varieties [ MR 862641 ]
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Dinakar Ramakrishnan — Analogs of the Bloch-Wigner function for higher polylogarithms [ MR 862642 ]
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Dinakar Ramakrishnan — Higher regulators on quaternionic Shimura curves and values of $L$-functions [ MR 862643 ]
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R. W. Thomason — Bott stability in algebraic $K$-theory [ MR 862644 ]
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This volume presents a state-of-the-art description of some of the exciting applications of algebraic \(K\)-theory to other branches of mathematics, especially algebraic geometry and algebraic number theory. As the proceedings of a 1983 AMS-IMS-SIAM Joint Summer Research Conference, it includes current and important work by some of the best researchers in the field. The diverse scope includes the following topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field to higher \(K\)-groups of varieties over number fields.
Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating \(K\)-theory to the Brauer group (as reported by Merkurjev and Wadsworth), and the papers by Kato on algebraic cycles.
Directed towards mathematicians working in algebraic \(K\)-theory, algebraic geometry, and algebraic number theory, this volume is also of interest to the algebraic topologist. The reader should be familiar with basic \(K\)-theory and interested in its applications to other areas of mathematics.
-
Articles
-
A. A. Beĭlinson — Higher regulators of modular curves [ MR 862627 ]
-
A. A. Beĭlinson — Notes on absolute Hodge cohomology [ MR 862628 ]
-
A. J. Berrick and M. E. Keating — The $K$-theory of triangular matrix rings [ MR 862629 ]
-
S. Bloch — A note on Gersten’s conjecture in the mixed characteristic case [ MR 862630 ]
-
S. Bloch and D. Grayson — $K_2$ and $L$-functions of elliptic curves: computer calculations [ MR 862631 ]
-
Dan Burghelea — Cyclic homology and the algebraic $K$-theory of spaces. I [ MR 862632 ]
-
Kevin R. Coombes — Local class field theory for curves [ MR 862633 ]
-
W. G. Dwyer and E. M. Friedlander — Conjectural calculations of general linear group homology [ MR 862634 ]
-
William G. Dwyer and Eric M. Friedlander — Some remarks on the $K$-theory of fields [ MR 862635 ]
-
Henri Gillet — The $K$-theory of twisted complexes [ MR 862636 ]
-
J. F. Jardine — Simplicial objects in a Grothendieck topos [ MR 862637 ]
-
Kazuya Kato — Milnor $K$-theory and the Chow group of zero cycles [ MR 862638 ]
-
Kazuya Kato and Shuji Saito — Global class field theory of arithmetic schemes [ MR 862639 ]
-
Aderemi O. Kuku — $K_n,\;SK_n$ of integral group-rings and orders [ MR 862640 ]
-
Claudio Pedrini and Charles A. Weibel — $K$-theory and Chow groups on singular varieties [ MR 862641 ]
-
Dinakar Ramakrishnan — Analogs of the Bloch-Wigner function for higher polylogarithms [ MR 862642 ]
-
Dinakar Ramakrishnan — Higher regulators on quaternionic Shimura curves and values of $L$-functions [ MR 862643 ]
-
R. W. Thomason — Bott stability in algebraic $K$-theory [ MR 862644 ]
