Download e-book for kindle: Algebraic K-groups as Galois modules by Victor P. Snaith

By Victor P. Snaith

ISBN-10: 3764367172

ISBN-13: 9783764367176

This monograph offers the state-of-the-art within the thought of algebraic K-groups. it really is of curiosity to a wide selection of graduate and postgraduate scholars in addition to researchers in comparable components akin to quantity idea and algebraic geometry. The thoughts provided listed below are largely algebraic or cohomological. all through quantity idea and arithmetic-algebraic geometry one encounters gadgets endowed with a normal motion via a Galois crew. specifically this is applicable to algebraic K-groups and ?tale cohomology teams. This quantity is anxious with the development of algebraic invariants from such Galois activities. quite often those invariants lie in low-dimensional algebraic K-groups of the indispensable group-ring of the Galois staff. A relevant subject matter, predictable from the Lichtenbaum conjecture, is the review of those invariants when it comes to specified values of the linked L-function at a destructive integer counting on the algebraic K-theory size. moreover, the "Wiles unit conjecture" is brought and proven to guide either to an review of the Galois invariants and to clarification of the Brumer-Coates-Sinnott conjectures. This publication is of curiosity to a wide selection of graduate and postgraduate scholars in addition to researchers in components relating to algebraic K-theory equivalent to quantity idea and algebraic geometry. The ideas offered listed below are mostly algebraic or cohomological. must haves on L-functions and algebraic K-theory are recalled whilst wanted.

Show description

Read or Download Algebraic K-groups as Galois modules PDF

Best algebra books

Download e-book for iPad: Algebra 08 by A. I. Kostrikin, I. R. Shafarevich

The monograph goals at a normal define of previous and new effects on representations of finite-dimensional algebras. In a concept which built speedily over the last 20 years, the shortcoming of textbooks is the most obstacle for rookies. consequently specific realization is paid to the rules, and proofs are integrated for statements that are straight forward, serve comprehension or are scarcely to be had.

Download PDF by Eric Jespers, Jan Okninski: Noetherian semigroup algebras (no pp. 10,28,42,53,60)

In the final decade, semigroup theoretical equipment have happened evidently in lots of elements of ring concept, algebraic combinatorics, illustration conception and their functions. specifically, inspired via noncommutative geometry and the speculation of quantum teams, there's a growing to be curiosity within the type of semigroup algebras and their deformations.

New PDF release: KVANT selecta: algebra and analysis, 1

The mathematics of binomial coefficients / D. B. Fuchs and M. B. Fuchs -- Do you love messing round with integers? / M. I. Bashmakov -- On Bertrand's conjecture / M. I. Bashmakov -- On top approximations, I-II / D. B. Fuchs and M. B. Fuchs -- On a definite estate of binomial coefficients / A. I. Shirshov -- On n!

Extra info for Algebraic K-groups as Galois modules

Sample text

When s = 0 = t these two groups differ by a uniquely divisible group and E:" = EL0. Since G(F/M) acts trivially on K3(Lo), E;" Hs(G(L/K); K3(Lo)) r Z/r 0 if s is odd, if s > 0 is even. Note also that H*(G(L/K); Lz) = 0 when L I K is totally ramified so that the sequence 2't-1 E Ellt if t is odd and s > 0. implies that ) H 2(G(F/E); K F d (Fo)) from Next we calculate H1 (G(F/E); K ? ~ ( F ~ ) and the exact sequence of [80]. The first group is isomorphic to the kernel of the map This homomorphism is an isomorphism on the uniquely divisible part, a surjection with kernel Z l r on the K2-part and the el-th power of the inclusion on the K1part.

2 Now we shall begin the construction of the local fundamental classes by considering the totally ramified case. 17 for finite Galois extensions of padic local fields. Furthermore, for K2r,K2r+1 with r 2 2 in this case we needed to assume that the Lichtenbaum-Quillen Conjecture ([I351 p. 326) was true for the mod p algebraic K-theory of p-adic local fields. When [135] was written this was known for 2-adic fields by [160]. For p-adic fields when p is odd the conjecture was proved recently [74]. When L I K is a Galois extension of local fields of characteristic p the Lichtenbaum-Quillen Conjecture is now known to be true by [60], which shows that the K-theory of L has no p-torsion, combined with the results of [148].

Therefore it remains to verify that G(L/K) - 1) 2 K2r-3(OL/~L) acts on z / ( v ( ~ - ' ) ~ via the quotient to G(W/K) whose generator acts by "multiplication" by vr-l, K ~ ~ - ~ ( Land o ) W. where v = IOK/nKI. Certainly, G(L/E) acts trivially on Chapter 3. Higher K-theory of Local Fields 70 Also the action by a E G(E/W) is trivial on the second coordinates in the direct sums. 1. 6) establishes the passage-toquotients part of the following result and the passage-to-subgroups is relatively straightforward.

Download PDF sample

Algebraic K-groups as Galois modules by Victor P. Snaith

by Thomas

Rated 4.13 of 5 – based on 31 votes