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

Semistable Symmetric Spectra in $A1$-homotopy theory