Noncommutative Iwasawa Main Conjectures over Totally Real - download pdf or read online

The algebraic suggestions built through Kakde will in all likelihood lead finally to significant development within the learn of congruences among automorphic types and the most conjectures of non-commutative Iwasawa idea for lots of factors. Non-commutative Iwasawa conception has emerged dramatically over the past decade, culminating within the contemporary facts of the non-commutative major conjecture for the Tate reason over a wholly genuine p-adic Lie extension of a bunch box, independently by means 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 found by means of Venjakob, and have been then systematically built  within the next papers by means of Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. there has been additionally parallel similar paintings during this path via Burns and Flach at the equivariant Tamagawa quantity conjecture. thus, Kato came across an enormous thought 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 facts is a gorgeous improvement of those rules of Kato, mixed with an concept 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 strategies of Frohlich and Taylor.
Since some of the principles during this ebook should still finally be acceptable to different reasons, one among its significant goals is to supply a self-contained exposition of a few of the most basic subject matters underlying those advancements. the current quantity may be a worthwhile source for researchers operating in either Iwasawa thought and the speculation of automorphic varieties.