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Hilbert modular forms and Iwasawa theory
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Catalogue Information
Field name
Details
Dewey Class
512.74 (DDC 23)
Title
Hilbert modular forms and Iwasawa theory ([EBook]) / Haruzo Hida
Author
Hida, Haruzo
Other name(s)
Oxford Scholarship Online
Publication
Oxford, U.K. : Oxford University Press , 2007
Physical Details
1 online resource
Series
Oxford mathematical monographs
ISBN
9780191718946
Note
Print publication date: 2006. - Published to Oxford Scholarship Online: September 2007
Summary Note
The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and applications of the theorem that have been found. Applications include a proof of the torsion of the adjoint Selmer group (over a totally real field F and over the Iwasawa tower of F) and an explicit formula of the L-invariant of the arithmetic p-adic adjoint L-functions. This implies the torsion of the classical anticyclotomic Iwasawa module of a CM field over the Iwasawa algebra. When specialized to an elliptic Tate curve over F by the L-invariant formula, the invariant of the adjoint square of the curve has exactly the same expression as the one in the conjecture of Mazur-Tate-Teitelbaum (which is for the standard L-function of the elliptic curve and is now a theorem of Greenberg-Stevens).:
Mode of acces to digital resource
Digital reproduction. Oxford : Oxford University Press, 2007. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher)
System details note
Online access to this digital book is restricted to subscribing institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1093/acprof:oso/9780198571025.001.0001
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Subject References:
Forms, Modular
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Hilbert modular surfaces
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Iwasawa theory
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Authors:
Hida, Haruzo
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Corporate Authors:
Oxford Scholarship Online
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Series:
Oxford mathematical monographs
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Classification:
512.74 (DDC 23)
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