There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
| ISBN: | 9781107492967 |
| Publication date: | 13th March 2015 |
| Author: | John University of Cambridge Coates |
| Publisher: | Cambridge University Press |
| Format: | Paperback |
| Pagination: | 320 pages |
| Series: | London Mathematical Society Lecture Note Series |
| Genres: |
Number theory Algebra |
There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
The Bloch–Kato Conjecture for the Riemann Zeta Function features in the following genres: Number theory, Algebra
The Bloch–Kato Conjecture for the Riemann Zeta Function is available in Paperback
The Bloch–Kato Conjecture for the Riemann Zeta Function was written by John University of Cambridge Coates and published by Cambridge University Press
The Bloch–Kato Conjecture for the Riemann Zeta Function has 320 pages
Yes it is part of London Mathematical Society Lecture Note Series series
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