Motivic Intersection Complex of Certain Shimura varieties

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Using a version of weight conservativity we demonstrate that for certain Shimura varieties (including all Shimura three-folds, most Shimura four-folds and the Siegel sixfold) the construction of the motivic intersection complex due to Wildeshaus compares with a motivic weight truncation in the sense of S. Morel. In particular it is defined up to a unique isomorphism, and satisfies the intrinsic characterization for an intermediate extension due to Wildeshaus.