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Timeline for Chow motive of a fibration

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Jun 29, 2014 at 14:44 comment added Matthias Wendt True, but for Hodge theory the global monodromy being trivial (as required in the question) would imply that the Leray-Serre spectral sequence degenerates. I think that there are two questions here: 1) is it possible to deform smooth projective varieties such that Chow groups change but the deformation is holomorphically trivial? 2) does trivial global monodromy in the analytic world imply trivial global monodromy in the motivic world? Both are interesting questions, but they sound like they are close to conservativity of deRham cohomology on motives...
Jun 29, 2014 at 14:23 history answered Victor Petrov CC BY-SA 3.0