Cyclotomic Fields and Zeta Values by John Coates (English) Hardcover Book

Description: Cyclotomic Fields and Zeta Values by John Coates, R. Sujatha Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely arithmetic expressions.Written by two leading workers in the field, this short and elegant book presents in full detail the simplest proof of the "main conjecture for cyclotomic fields. Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. The masterly exposition is intended to be accessible to both graduatestudents and non-experts in Iwasawa theory. Notes Presents in full detail the simplest proof of the "main conjecture" for cyclotomic fieldsWritten by two leading figures in the fieldAccessible to both graduate students and non-experts in Iwasawa theory Back Cover Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely arithmetic expressions (the most celebrated example being the conjecture of Birch and Swinnerton-Dyer for elliptic curves). Written by two leading workers in the field, this short and elegant book presents in full detail the simplest proof of the "main conjecture for cyclotomic fields . Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. The masterly exposition is intended to be accessible to both graduate students and non-experts in Iwasawa theory. Author Biography Lieutenant-General John Coates served in the Australian Army for forty years, retiring as Chief of the General Staff in 1992. He commanded a Calvary (Armoured Personnel Carrier) Squadron in South Vietnam in 1970 -1971, for which service he was made a Member of the Order of the British Empire (MBE). He was made a Companion of the Order of Australia (AC) IN 1992. He has a post-graduate degree in history from the Australian National University. Table of Contents Cyclotomic Fields.- Local Units.- Iwasawa Algebras and p-adic Measures.- Cyclotomic Units and Iwasawas Theorem.- Euler Systems.- Main Conjecture. Review From the reviews:"The authors aim in this book is to present a proof of the so-called Iwasawa Main Conjecture for the pth cyclotomic field … . The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details. According to the authors, the book is intended for graduate students and the non-expert in Iwasawa theory. I think that also the expert may enjoy reading this kind of unified treatment of such a beautiful theme." (Tauno Metsänkylä, Zentralblatt MATH, Vol. 1100 (2), 2007)"This book was written to present in full detail a complete proof of the so-called Main Conjecture in the arithmetic theory of cyclotomic fields. … The book is intended for graduate students and the non-expert in Iwasawa theory; however, the expert will find this work a valuable source in the arithmetic theory of cyclotomic fields. The book is very pleasant to read and is written with enough detail … . The authors havecontributed in an important way to Iwasawa theory with this beautiful book." (Gabriel D. Villa-Salvador, Mathematical Reviews, Issue 2007 g)"The aim of this monograph is to present a detailed proof of the Main Conjecture, described by the authors as the deepest result we know about the arithmetic of cyclotomic fields. … This beautiful book will enable non-experts to study a state-of-the-art proof of the Main Conjecture. Furthermore, it might be a source of inspiration for new generations of mathematicians trying to tackle one of the many similar relations conjectured to hold in arithmetic geometry." (Ch. Baxa, Monatshefte fÜr Mathematik, Vol. 154 (1), May, 2008) Long Description Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely arithmetic expressions. Written by two leading workers in the field, this short and elegant book presents in full detail the simplest proof of the "main conjecture for cyclotomic fields. Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. The masterly exposition is intended to be accessible to both graduate students and non-experts in Iwasawa theory. Review Quote From the reviews: "The authors aim in this book is to present a proof of the so-called Iwasawa Main Conjecture for the pth cyclotomic field ... . The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details. According to the authors, the book is intended for graduate students and the non-expert in Iwasawa theory. I think that also the expert may enjoy reading this kind of unified treatment of such a beautiful theme." (Tauno Metsnkyl, Zentralblatt MATH, Vol. 1100 (2), 2007) "This book was written to present in full detail a complete proof of the so-called Main Conjecture in the arithmetic theory of cyclotomic fields. ... The book is intended for graduate students and the non-expert in Iwasawa theory; however, the expert will find this work a valuable source in the arithmetic theory of cyclotomic fields. The book is very pleasant to read and is written with enough detail ... . The authors have contributed in an important way to Iwasawa theory with this beautiful book." (Gabriel D. Villa-Salvador, Mathematical Reviews, Issue 2007 g) "The aim of this monograph is to present a detailed proof of the Main Conjecture, described by the authors as the deepest result we know about the arithmetic of cyclotomic fields. ... This beautiful book will enable non-experts to study a state-of-the-art proof of the Main Conjecture. Furthermore, it might be a source of inspiration for new generations of mathematicians trying to tackle one of the many similar relations conjectured to hold in arithmetic geometry." (Ch. Baxa, Monatshefte fr Mathematik, Vol. 154 (1), May, 2008) Feature Presents in full detail the simplest proof of the "main conjecture" for cyclotomic fields Written by two leading figures in the field Accessible to both graduate students and non-experts in Iwasawa theory Details ISBN3540330682 Author R. Sujatha Short Title CYCLOTOMIC FIELDS & ZETA VALUE Series Springer Monographs in Mathematics Language English ISBN-10 3540330682 ISBN-13 9783540330684 Media Book Format Hardcover Year 2006 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Pages 116 Illustrations X, 116 p. DOI 10.1604/9783540330684;10.1007/978-3-540-33069-1 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2006 ed. Edition 2006th Publication Date 2006-08-18 Alternative 9783642069598 DEWEY 512.7 Audience Undergraduate We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96226274;

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