Posted in Algebra

New PDF release: Invitation to Higher Local Feilds

By I. Fesenko, M. Kurihara

Show description

Read or Download Invitation to Higher Local Feilds PDF

Similar algebra books

Read e-book online Making Groups Work: Rethinking Practice PDF

Such a lot people paintings in them, such a lot folks reside in them. a few are advanced, a few are uncomplicated. a few meet just once whereas others final for many years. no matter what shape they take, teams are critical to our lives. Making teams paintings bargains a entire creation to the most important concerns in crew paintings. It outlines the position of teams and the heritage of staff paintings, discusses staff politics, and indicates how teams may also help advertise social swap.

Additional info for Invitation to Higher Local Feilds

Example text

At first sight this question looks trivial because the group DKn (F ) consists of all divisible elements of Kn (F ) . However, the following theorem shows that the group DKn (F ) is not necessarily a divisible group! Theorem 8 (Izhboldin, [ I3 ]). For every n > 2 and prime p there is a field F such that char (F ) 6= p , p 2 F and (1) The group DKn (F ) is not divisible, and the group Dp K2 (F ) is not p -divisible, Geometry & Topology Monographs, Volume 3 (2000) – Invitation to higher local fields 28 O.

Math. IHES 63(1986), 107–152. H. Bass, H. and J. Tate, The Milnor ring of a global field, In Algebraic K -theory II, Lect. Notes in Math. 342, Springer-Verlag, Berlin, 1973, 349–446. I. Fesenko, Class field theory of multidimensional local fields of characteristic 0, with the residue field of positive characteristic, Algebra i Analiz (1991); English translation in St. Petersburg Math. J. 3(1992), 649–678. Geometry & Topology Monographs, Volume 3 (2000) – Invitation to higher local fields Part I.

2. Tate’s argument. To prove Bloch–Kato’s theorem we may assume that Indeed, consider the cohomological long exact sequence n = 1. p q ! H q;1 (K Z=p(q)) ;! H q (K Z=pn;1(q)) ;! H (K Z=pn(q)) ! : : : which comes from the Bockstein sequence 0 ;! Z=pn;1 ; ! Z=pn ;;;! Z=p ;! 0: p mod p We may assume p 2 K , so H q;1 (K Z=p(q )) ' hq;1 (K ) and the following diagram is commutative (cf. [ T, x2 ]): g kq;1 (K ) ;f;;;p! yhq; 1 K Kq (K )=pn;1 ? hq K ? y p ;;;; ! Kq (K )=pn ? hq K ? y mod p ;;;; ! kq (K ) ?

Download PDF sample

Invitation to Higher Local Feilds by I. Fesenko, M. Kurihara


by Mark
4.1

Rated 4.95 of 5 – based on 33 votes