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<図書>
Twisted L-functions and monodromy

責任表示 by Nicholas M. Katz
シリーズ Annals of mathematics studies ; no. 150
データ種別 図書
出版者 Princeton, N.J. : Princeton University Press
出版年 2002
本文言語 英語
大きさ viii, 249 p. ; 24 cm
概要 For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the...work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
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所蔵情報

: hbk 理系図3F 数理独自 023212002000990 KATZ/20/5 2002

書誌詳細

一般注記 Bibliography: p. [235]-239
Includes index
著者標目 *Katz, Nicholas M., 1943-
件 名 LCSH:L-functions
LCSH:Monodromy groups
分 類 LCC:QA246
DC21:512/.74
書誌ID 1001404035
ISBN 0691091501
NCID BA55306535
巻冊次 : cloth ; ISBN:0691091501
: pbk ; ISBN:069109151X
登録日 2009.11.02
更新日 2009.11.02

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