By John Coates,Peter Schneider,Sujatha Ramdorai,Otmar Venjakob
The algebraic innovations built through Kakde will possibly lead finally to significant development within the examine of congruences among automorphic types and the most conjectures of non-commutative Iwasawa concept for lots of factors. Non-commutative Iwasawa conception has emerged dramatically during the last decade, culminating within the fresh facts of the non-commutative major conjecture for the Tate reason over a unconditionally genuine p-adic Lie extension of a bunch box, independently by way of Ritter and Weiss at the one hand, and Kakde at the different. The preliminary principles for giving an exact formula of the non-commutative major conjecture have been chanced on by means of Venjakob, and have been then systematically constructed within the next papers by means of Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. there has been additionally parallel similar paintings during this course via Burns and Flach at the equivariant Tamagawa quantity conjecture. for that reason, Kato found an enormous concept for learning the K_1 teams of non-abelian Iwasawa algebras when it comes to the K_1 teams of the abelian quotients of those Iwasawa algebras. Kakde's evidence is a gorgeous improvement of those principles of Kato, mixed with an idea of Burns, and basically reduces the examine of the non-abelian major conjectures to abelian ones. The procedure of Ritter and Weiss is extra classical, and partially encouraged via concepts of Frohlich and Taylor.
Since a few of the principles during this e-book may still ultimately be appropriate to different explanations, one among its significant goals is to supply a self-contained exposition of a few of the most normal topics underlying those advancements. the current quantity should be a necessary source for researchers operating in either Iwasawa idea and the idea of automorphic types.
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