Arapura gives a simpler construction of motivic sheaves and a simpler proof that the Leray spectral sequence has a motivic lift whose Betti realization is the classical Leray spectral sequence.
Dimca, Sheaves in topology, Springer (2004)
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Motivic sheaves revisited
Arapura gives a simpler construction of motivic sheaves and a simpler proof that the Leray spectral sequence has a motivic lift whose Betti realization is the classical Leray spectral sequence.