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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
Links to Related Works	Subject References: Forms, Modular . Hilbert modular surfaces . Iwasawa theory . Authors: Hida, Haruzo . Corporate Authors: Oxford Scholarship Online . Series: Oxford mathematical monographs . Classification: 512.74 (DDC 23) .

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Hilbert modular forms and Iwasawa theory

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