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Finite dimensional objects in distinguished triangles

Vladimir Guletskii
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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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Vladimir Guletskii. 2003-06-19. Finite dimensional objects in distinguished triangles. https://arxiv.org/abs/math/0306297

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