New York Journal of Mathematics
Volume 21 (2015) 1-56


Stephan Hähne and Jens Hornbostel

Semistable symmetric spectra in A1-homotopy theory

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Published: January 9, 2015
Keywords: semistable symmetric spectra, stable motivic homotopy theory
Subject: 14F42, 55P43

We study semistable symmetric spectra based on quite general monoidal model categories, including motivic examples. In particular, we establish a generalization of Schwede's list of equivalent characterizations of semistability in the case of motivic symmetric spectra. We also show that the motivic Eilenberg-MacLane spectrum and the algebraic cobordism spectrum are semistable. Finally, we show that semistability is preserved under localization if some reasonable conditions -- which often hold in practice -- are satisfied.

Author information

Stephan Hähne:
Groenenweg 79, 22549 Hamburg

Jens Hornbostel:
Bergische Universität Wuppertal, FB C, Mathematik und Informatik, Gaussstrasse 20, 42119 Wuppertal