Nil k-theory maps to cyclic homology

Charles A. Weibel

doi:10.1090/S0002-9947-1987-0902784-0

Nil k-theory maps to cyclic homology

Charles A. Weibel

SAS - Mathematics

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

19 Scopus citations

Abstract

Algebraic K-theory breaks into two pieces: nil if-theory and Karoubi-Villamayor K-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil if-theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.

Original language	English (US)
Pages (from-to)	541-558
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	303
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1987-0902784-0
State	Published - Oct 1987

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Algebraic K-theory. Partially supported by NSF grant
Cyclic homology

Access to Document

10.1090/S0002-9947-1987-0902784-0

Cite this

@article{ec5ec8fbc5a443baa41c3afc28da44ce,

title = "Nil k-theory maps to cyclic homology",

abstract = "Algebraic K-theory breaks into two pieces: nil if-theory and Karoubi-Villamayor K-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil if-theory to cyclic homology which are compatible with Karoubi{\textquoteright}s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.",

keywords = "Algebraic K-theory. Partially supported by NSF grant, Cyclic homology",

author = "Weibel, {Charles A.}",

year = "1987",

month = oct,

doi = "10.1090/S0002-9947-1987-0902784-0",

language = "English (US)",

volume = "303",

pages = "541--558",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Nil k-theory maps to cyclic homology

AU - Weibel, Charles A.

PY - 1987/10

Y1 - 1987/10

N2 - Algebraic K-theory breaks into two pieces: nil if-theory and Karoubi-Villamayor K-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil if-theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.

AB - Algebraic K-theory breaks into two pieces: nil if-theory and Karoubi-Villamayor K-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil if-theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.

KW - Algebraic K-theory. Partially supported by NSF grant

KW - Cyclic homology

UR - http://www.scopus.com/inward/record.url?scp=84966251281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966251281&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1987-0902784-0

DO - 10.1090/S0002-9947-1987-0902784-0

M3 - Article

AN - SCOPUS:84966251281

VL - 303

SP - 541

EP - 558

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -

Nil k-theory maps to cyclic homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this