Semistable Symmetric Spectra in $A1$-homotopy theory

Stephan Haehne, Jens Hornbostel

Published 2013-12-16, updated 2014-04-16Version 2

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.