It was proven in section 5.3 of BBD (see Corollary 5.3.2) that for an open immersion $j$ the functor $j_{!*}$ respects preserves weights of mixed sheaves. The proof relies on several previous results; it is especially complicated in the case when $j$ is not affine. Does an easier proof (or a plan of it:)) exist? I would like to have a proof that (mostly) relies on the properties of $j_{!*}$ (and on the 'formal' properties of weights).
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Is there an easy proof of the fact that the intermeidate intermediate image functor respects weights? |
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Is there an easy proof of the fact that the intermeidate image functor respects weights?It was proven in section 5.3 of BBD that for an open immersion $j$ the functor $j_{!*}$ respects weights of mixed sheaves. The proof relies on several previous results; it is especially complicated in the case when $j$ is not affine. Does an easier proof (or a plan of it:)) exist?
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