Finite-dimensional objects in distinguished triangles Original Research Article

Let image be a image-linear closed symmetric monoidal triangulated category in the sense of [M. Hovey, Model Categories, Math. Surveys Monogr., vol. 63, Amer. Math. Soc., Providence, RI, 1999]. We prove an additivity for evenly and oddly finite-dimensional vertices of distinguished triangles in image (Theorem 1). As a corollary, we get motivic finite dimensionality for quasi-projective curves over a field (Theorem 3). The last result has been independently obtained by C. Mazza, see [C. Mazza, Schur functors and motives, preprint, 2003, http://www.math.uiuc.edu/K-theory/0641/].