Finite dimensional objects in distinguished triangles, by Vladimir Guletskii

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.

[Updated June 20, 2003: contains additional citations and corrections of misprints.]

[Updated Jan 5, 2004: should be clearer and more readable now.]


Vladimir Guletskii <guletskii@im.bas-net.by, vladimir.guletskii@mathematik.uni-regensburg.de>