Positive Model Structures for Abstract Symmetric Spectra

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Abstract

We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn’s sense, of a certain positive projective model structure on spectra, where positivity basically means the truncation of the zero level. The localization is by the set of stabilizing morphisms or their truncated version.

Keywords

Symmetric monoidal model category Cofibrantly generated model category Localization of a model structure Quillen functors Symmetric spectra Stable model structure Stable homotopy category 

Mathematics Subject Classification (2010)

18D10 18G55 

Notes

Acknowledgments

Open access funding provided by University of Liverpool. The authors are grateful to Peter May, who has drawn our attention to positive model structures in topology, and to Joseph Ayoub for useful comments on homotopy type under the action of finite groups. We are also grateful to the anonymous referee whose comments helped to improve the exposition. The paper is written in the framework of the EPSRC grant EP/I034017/1. The first named author acknowledges the support of the grants MK-5215.2015.1, RFBR 14-01-00178, Dmitry Zimin’s Dynasty Foundation and Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. No.14.641.31.0001.

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of Economics, Russian Federation, Laboratory of Mirror Symmetry, NRU HSEMoscowRussia
  3. 3.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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