Abstract
We prove an additivity for evenly (oddly) finite dimensional objects in distinguished triangles in a triangulated monoidal category structured by an underlying model monoidal category. In particular, the result holds in the Q-localized motivic stable homotopy category of spectra and in Q-localized Voevodsky's category of motives over a field, char=0. As an application, we show that the motives of schemes of dimension one (separated and of finite type over a field, char=0) are finite dimensional.
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