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The Bloch–Kato Conjecture for the Riemann Zeta Function: London Mathematical Society Lecture Note Series, cartea 418

Editat de John Coates, A. Raghuram, Anupam Saikia, R. Sujatha
en Limba Engleză Paperback – 13 mar 2015
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.
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Specificații

ISBN-13: 9781107492967
ISBN-10: 1107492963
Pagini: 320
Dimensiuni: 153 x 228 x 18 mm
Greutate: 0.45 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria London Mathematical Society Lecture Note Series

Locul publicării:New York, United States

Cuprins

List of contributors; Preface A. Raghuram; 1. Special values of the Riemann zeta function: some results and conjectures A. Raghuram; 2. K-theoretic background R. Sujatha; 3. Values of the Riemann zeta function at the odd positive integers and Iwasawa theory John Coates; 4. Explicit reciprocity law of Bloch–Kato and exponential maps Anupam Saikia; 5. The norm residue theorem and the Quillen–Lichtenbaum conjecture Manfred Kolster; 6. Regulators and zeta functions Stephen Lichtenbaum; 7. Soulé's theorem Stephen Lichtenbaum; 8. Soulé's regulator map Ralph Greenberg; 9. On the determinantal approach to the Tamagawa number conjecture T. Nguyen Quang Do; 10. Motivic polylogarithm and related classes Don Blasius; 11. The comparison theorem for the Soulé–Deligne classes Annette Huber; 12. Eisenstein classes, elliptic Soulé elements and the ℓ-adic elliptic polylogarithm Guido Kings; 13. Postscript R. Sujatha.

Descriere

A graduate-level account of an important recent result concerning the Riemann zeta function.