weight (awaiting review)

Associated to a motive are vector spaces coming from cohomology $H^*(X)$ of an algebraic variety $X$. If these vector spaces arise in $H^w(X)$, then $w$ is the (motivic) weight of the motive. The weight is the number of commas in the Hodge vector, i.e., the Hodge vector is of the form $(h^{0,w},\dots,h^{w,0})$.