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001 978-3-642-32199-3
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008 121026s2013 gw | s |||| 0|eng d
020 _a9783642321993
_9978-3-642-32199-3
024 7 _a10.1007/978-3-642-32199-3
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
245 1 0 _aNoncommutative Iwasawa Main Conjectures over Totally Real Fields
_h[electronic resource] :
_bM�nster, April 2011 /
_cedited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXII, 208 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Proceedings in Mathematics & Statistics,
_x2194-1009 ;
_v29
505 0 _aPreface -- John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non-commutative main conjectures for totally real fields -- �R. Sujatha: Reductions of the main conjecture -- Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present -- Peter Schneider, Otmar Venjakob: �K_1 of certain Iwasawa algebras, after Kakde -- Mahesh Kakde: Congruences between abelian p-adic zeta functions -- Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach -- �Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory.
520 _aThe algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developed� in the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered an important idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with an idea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The approach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideas in this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of some of the main general themes underlying these developments. The present volume will be a valuable resource for researchers working in both Iwasawa theory and the theory of automorphic forms.�.
650 0 _aMathematics.
650 0 _aAlgebraic geometry.
650 0 _aK-theory.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aK-Theory.
700 1 _aCoates, John.
_eeditor.
700 1 _aSchneider, Peter.
_eeditor.
700 1 _aSujatha, R.
_eeditor.
700 1 _aVenjakob, Otmar.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642321986
830 0 _aSpringer Proceedings in Mathematics & Statistics,
_x2194-1009 ;
_v29
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-32199-3
912 _aZDB-2-SMA
999 _c199250
_d199250