Torsion Motives

Abstract In this paper, we study Chow motives whose identity map is killed by a natural number. Examples of such objects were constructed Gorchinskiy and Orlov [ 10]. We introduce various invariants torsion motives, in particular, the $p$-level. show that invariant bounds from below dimension variety motive $M$ direct summand imposes restrictions on motivic singular cohomology $M$. more details $p$-torsion surfaces, Godeaux motive. are $1$-to-$1$ correspondence with certain Rost cycle submodules free modules over $H^*_{et}$. This description parallel to mod-$p$ reduced curves.