[-- This version fixes some typos and has an introduction. The exposition of the last part has been clarified. --]
In this article we study the class of Schur-finite motives, that is, motives which are annihilated by a Schur functor. We proceed to analyze the relations between this notion and a similar one due to Kimura. We conclude by applying this notion to the category DM and proving that the motive of any curve is Kimura-finite.
This last result has also been obtained by V. Guletskii.