TL;DR
This paper investigates Schur-finite motives, comparing them to Kimura-finite motives, and provides examples illustrating their properties and differences, including the finiteness of motives of curves and a non-Kimura-finite Schur-finite motive.
Contribution
It introduces and compares Schur-finite and Kimura-finite motives, proving the motive of any curve is Kimura-finite and providing an example of a Schur-finite but non-Kimura-finite motive.
Findings
Motive of any curve is Kimura-finite
Schur-finite motives include some non-Kimura-finite motives
Comparison between Schur-finite and Kimura-finite motives
Abstract
In this article we study the class of Schur-finite motives, that is, motives which are annihilated by a Schur functor. We compare this notion to a similar one due to Kimura. In particular, we show that the motive of any curve is Kimura-finite. This last result has also been obtained by V. Guletskii. We conclude with an example by O'Sullivan of a non Kimura-finite motive which is Schur-finite.
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