Étale descent for two-primary algebraic K-theory of totally imaginary number fields

J. Rognes; C. Weibel

doi:10.1023/A:1007751307676

Étale descent for two-primary algebraic K-theory of totally imaginary number fields

J. Rognes, C. Weibel

School of Arts and Sciences, Mathematics

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

9 Scopus citations

Abstract

We show that the natural map from 2-adic algebraic K-theory to 2-adic étale K-theory induces an isomorphism in positive degrees for rings of 2-integers in totally imaginary number fields. In this sense, 2-adic algebraic K-theory of totally imaginary number fields satisfies étale descent in positive degrees.

Original language	English (US)
Pages (from-to)	101-104
Number of pages	4
Journal	K-Theory
Volume	16
Issue number	2
DOIs	https://doi.org/10.1023/A:1007751307676
State	Published - 1999

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Algebraic K-theory
Bloch-Lichtenbaum spectral sequence
Dwyer-friedlander spectral sequence
Étale K-theory
Étale descent

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10.1023/A:1007751307676

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title = "{\'E}tale descent for two-primary algebraic K-theory of totally imaginary number fields",

abstract = "We show that the natural map from 2-adic algebraic K-theory to 2-adic {\'e}tale K-theory induces an isomorphism in positive degrees for rings of 2-integers in totally imaginary number fields. In this sense, 2-adic algebraic K-theory of totally imaginary number fields satisfies {\'e}tale descent in positive degrees.",

keywords = "Algebraic K-theory, Bloch-Lichtenbaum spectral sequence, Dwyer-friedlander spectral sequence, {\'E}tale K-theory, {\'E}tale descent",

author = "J. Rognes and C. Weibel",

year = "1999",

doi = "10.1023/A:1007751307676",

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T1 - Étale descent for two-primary algebraic K-theory of totally imaginary number fields

AU - Rognes, J.

AU - Weibel, C.

PY - 1999

Y1 - 1999

N2 - We show that the natural map from 2-adic algebraic K-theory to 2-adic étale K-theory induces an isomorphism in positive degrees for rings of 2-integers in totally imaginary number fields. In this sense, 2-adic algebraic K-theory of totally imaginary number fields satisfies étale descent in positive degrees.

AB - We show that the natural map from 2-adic algebraic K-theory to 2-adic étale K-theory induces an isomorphism in positive degrees for rings of 2-integers in totally imaginary number fields. In this sense, 2-adic algebraic K-theory of totally imaginary number fields satisfies étale descent in positive degrees.

KW - Algebraic K-theory

KW - Bloch-Lichtenbaum spectral sequence

KW - Dwyer-friedlander spectral sequence

KW - Étale K-theory

KW - Étale descent

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JO - K-Theory

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IS - 2

ER -

Étale descent for two-primary algebraic K-theory of totally imaginary number fields

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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