Homology of the full linear group over a local ring, and milnor's k-theory

Yu P. Nesterenko; A. A. Suslin

doi:10.1070/IM1990v034n01ABEH000610

Homology of the full linear group over a local ring, and milnor's k-theory

Yu P. Nesterenko, A. A. Suslin

Mathematics

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

For rings with a large number of units the authors prove a strengthened theoremon homological stabilization: the homomorphism H_k(GL_n(A)) 薔 H_k(GL(A)) is surjective for n 蠅 k + sr A 舑 1 and bijective for n 蠅 k + sr A. If A is a local ring with an infinite residue field, then this result admits further refinement:the homomorphism H_n(GL_n(A)) 薔 H_n(GL(A)) is bijective and the factor group H_n(GL(A))/H_n(GL_{n -1}(A)) is canonically isomorphic to Milnor's nth K-group of the ring A. The results are applied to compute the Chow groups of algebraic varieties.

Original language	English (US)
Pages (from-to)	121-145
Number of pages	25
Journal	Mathematics of the USSR - Izvestija
Volume	34
Issue number	1
DOIs	https://doi.org/10.1070/IM1990v034n01ABEH000610
State	Published - Feb 28 1990

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1070/IM1990v034n01ABEH000610

Cite this

@article{bfdef0bd42114ab4a1a871c25eb12967,

title = "Homology of the full linear group over a local ring, and milnor's k-theory",

abstract = "For rings with a large number of units the authors prove a strengthened theoremon homological stabilization: the homomorphism Hk(GLn(A)) 薔 Hk(GL(A)) is surjective for n 蠅 k + sr A 舑 1 and bijective for n 蠅 k + sr A. If A is a local ring with an infinite residue field, then this result admits further refinement:the homomorphism Hn(GLn(A)) 薔 Hn(GL(A)) is bijective and the factor group Hn(GL(A))/Hn(GLn -1(A)) is canonically isomorphic to Milnor's nth K-group of the ring A. The results are applied to compute the Chow groups of algebraic varieties.",

author = "Nesterenko, {Yu P.} and Suslin, {A. A.}",

year = "1990",

month = feb,

day = "28",

doi = "10.1070/IM1990v034n01ABEH000610",

language = "English (US)",

volume = "34",

pages = "121--145",

journal = "Izvestiya Mathematics",

issn = "1064-5632",

publisher = "IOP Publishing Ltd.",

number = "1",

}

TY - JOUR

T1 - Homology of the full linear group over a local ring, and milnor's k-theory

AU - Nesterenko, Yu P.

AU - Suslin, A. A.

PY - 1990/2/28

Y1 - 1990/2/28

N2 - For rings with a large number of units the authors prove a strengthened theoremon homological stabilization: the homomorphism Hk(GLn(A)) 薔 Hk(GL(A)) is surjective for n 蠅 k + sr A 舑 1 and bijective for n 蠅 k + sr A. If A is a local ring with an infinite residue field, then this result admits further refinement:the homomorphism Hn(GLn(A)) 薔 Hn(GL(A)) is bijective and the factor group Hn(GL(A))/Hn(GLn -1(A)) is canonically isomorphic to Milnor's nth K-group of the ring A. The results are applied to compute the Chow groups of algebraic varieties.

AB - For rings with a large number of units the authors prove a strengthened theoremon homological stabilization: the homomorphism Hk(GLn(A)) 薔 Hk(GL(A)) is surjective for n 蠅 k + sr A 舑 1 and bijective for n 蠅 k + sr A. If A is a local ring with an infinite residue field, then this result admits further refinement:the homomorphism Hn(GLn(A)) 薔 Hn(GL(A)) is bijective and the factor group Hn(GL(A))/Hn(GLn -1(A)) is canonically isomorphic to Milnor's nth K-group of the ring A. The results are applied to compute the Chow groups of algebraic varieties.

UR - http://www.scopus.com/inward/record.url?scp=84956133370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956133370&partnerID=8YFLogxK

U2 - 10.1070/IM1990v034n01ABEH000610

DO - 10.1070/IM1990v034n01ABEH000610

M3 - Article

AN - SCOPUS:84956133370

SN - 1064-5632

VL - 34

SP - 121

EP - 145

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

IS - 1

ER -

Homology of the full linear group over a local ring, and milnor's k-theory

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this