Homotopical localizations of module spectra

Carles Casacuberta; Javier J. Gutiérrez

doi:10.1090/S0002-9947-04-03552-4

Homotopical localizations of module spectra

Carles Casacuberta, Javier J. Gutiérrez

Department of Mathematics

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

11 Citations (Scopus)

Abstract

We prove that stable f-localizations (where f is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg-Mac Lane spectrum HZ. As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations. © 2004 American Mathematical Society.

Original language	English
Pages (from-to)	2753-2770
Journal	Transactions of the American Mathematical Society
Volume	357
DOIs	https://doi.org/10.1090/S0002-9947-04-03552-4
Publication status	Published - 1 Jul 2005

Keywords

Localization
Module spectrum
Ring spectrum
Stable GEM

Access to Document

10.1090/S0002-9947-04-03552-4

Cite this

@article{d87e93bffbad4f12806f82d0f41af0ff,

title = "Homotopical localizations of module spectra",

abstract = "We prove that stable f-localizations (where f is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg-Mac Lane spectrum HZ. As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations. {\textcopyright} 2004 American Mathematical Society.",

keywords = "Localization, Module spectrum, Ring spectrum, Stable GEM",

author = "Carles Casacuberta and Guti{\'e}rrez, \{Javier J.\}",

year = "2005",

month = jul,

day = "1",

doi = "10.1090/S0002-9947-04-03552-4",

language = "English",

volume = "357",

pages = "2753--2770",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Homotopical localizations of module spectra

AU - Casacuberta, Carles

AU - Gutiérrez, Javier J.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - We prove that stable f-localizations (where f is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg-Mac Lane spectrum HZ. As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations. © 2004 American Mathematical Society.

AB - We prove that stable f-localizations (where f is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg-Mac Lane spectrum HZ. As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations. © 2004 American Mathematical Society.

KW - Localization

KW - Module spectrum

KW - Ring spectrum

KW - Stable GEM

UR - https://www.scopus.com/pages/publications/22544483533

U2 - 10.1090/S0002-9947-04-03552-4

DO - 10.1090/S0002-9947-04-03552-4

M3 - Article

SN - 0002-9947

VL - 357

SP - 2753

EP - 2770

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Homotopical localizations of module spectra

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this