Articles liés à Twisted L-Functions and Monodromy.

Twisted L-Functions and Monodromy. - Couverture souple

Livre 20 sur 202: Annals of Mathematics Studies

Katz, Nicholas M.

 
9780691091518: Twisted L-Functions and Monodromy.
Couverture souple
ISBN 10 : 069109151X ISBN 13 : 9780691091518
Editeur : Princeton University Press, 2002

Synopsis

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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À propos de l'auteur

Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of four other books in this series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; and Rigid Local Systems.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2002
Langue
anglais
ISBN 10 
069109151X
ISBN 13 
9780691091518
Reliure
Broché
Nombre de pages
246
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9780691091501: Twisted L-functions and Monodromy

Edition présentée

ISBN 10 :  0691091501 ISBN 13 :  9780691091501
Editeur : Princeton University Press, 2002
Couverture rigide