Detecting effectivity of motives, their weights, connectivity, and dimension via Chow-weight (co)homology: a "mixed motivic decomposition of the diagonal"

Mikhail V. Bondarko, Vladimir A. Sosnilo

We describe certain criteria for a motif $M$ to be $r$-effective, i.e., to belong to the $r$th Tate twist $ObjD{M}_{gm,R}^{eff}(r)=ObjD{M}_{gm,R}^{eff}\otimes L^{\otimes r}$ of effe…