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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 $(h^{0,w},\dots,h^{w,0})$.

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• Last edited by Edgar Costa on 2020-02-17 18:41:55
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