Format:
Online-Ressource (237 p.)
Edition:
Online-Ausg.
ISBN:
9781400824885
Series Statement:
Annals of Mathematics Studies v.v. 150
Content:
Cover; Title Page; Copyright Page; Table of Contents; Introduction; Part I: Background Material; Appendix to Chapter 1: A Result of Zalesskii; Chapter 2: Lefschetz Pencils, Especially on Cur; Chapter 3: Induction; Chapter 4: Middle Convolution; Part II: Twist Sheaves, over an Algebraically Closed Field; Chapter 5: Twist Sheaves and Their Monodromy; Part III: Twist Sheaves, over a Finite Field; Chapter 6: Dependence on Parameters; Chapter 7: Diophantine Applications over a Finite Field; Chapter 8: Average Order of Zero in Twist Families. - Part IV: Twist Sheaves, over Schemes of Finite Type over ZChapter 9: Twisting by ""Primes"", and Working over Z; Chapter 10: Horizontal Results; References; Index. - 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 curve
Content:
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 th
Note:
Description based upon print version of record
,
Cover; Title Page; Copyright Page; Table of Contents; Introduction; Part I: Background Material; Appendix to Chapter 1: A Result of Zalesskii; Chapter 2: Lefschetz Pencils, Especially on Cur; Chapter 3: Induction; Chapter 4: Middle Convolution; Part II: Twist Sheaves, over an Algebraically Closed Field; Chapter 5: Twist Sheaves and Their Monodromy; Part III: Twist Sheaves, over a Finite Field; Chapter 6: Dependence on Parameters; Chapter 7: Diophantine Applications over a Finite Field; Chapter 8: Average Order of Zero in Twist Families
,
Part IV: Twist Sheaves, over Schemes of Finite Type over ZChapter 9: Twisting by "Primes", and Working over Z; Chapter 10: Horizontal Results; References; Index;
Additional Edition:
ISBN 0691091501
Additional Edition:
ISBN 069109151X
Additional Edition:
Erscheint auch als Druck-Ausgabe Katz, Nicholas M., 1943 - Twisted L-functions and monodromy Princeton : Princeton University Press, 2002 ISBN 0691091501
Additional Edition:
ISBN 069109151X
Language:
English
Subjects:
Mathematics
Keywords:
Elliptische Kurve
;
L-Funktion
;
Monodromie
;
L-Funktion
;
Monodromiegruppe
;
Electronic books
Author information:
Katz, Nicholas M. 1943-
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