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Cyclotomic Fields and Zeta Values

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Written by two leading workers in the field, this brief but elegant book presents in full detail the simplest proof of the "main ... Weiterlesen
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Beschreibung

Written by two leading workers in the field, this brief but 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.

From the reviews: "The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details." --ZENTRALBLATT MATH



Klappentext

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.



Inhalt
Cyclotomic Fields.- Local Units.- Iwasawa Algebras and p-adic Measures.- Cyclotomic Units and Iwasawa's Theorem.- Euler Systems.- Main Conjecture.

Produktinformationen

Titel: Cyclotomic Fields and Zeta Values
Autor:
EAN: 9783540330691
ISBN: 978-3-540-33069-1
Digitaler Kopierschutz: Wasserzeichen
Format: E-Book (pdf)
Hersteller: Springer Berlin Heidelberg
Herausgeber: Springer
Genre: Grundlagen
Anzahl Seiten: 116
Veröffentlichung: 03.10.2006
Jahr: 2006
Dateigrösse: 2.3 MB

Weitere Bände aus der Buchreihe "Springer Monographs in Mathematics"