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Jan 24, 2015 at 23:25 vote accept Mikhail Bondarko
Mar 24, 2014 at 18:34 comment added Mikhail Bondarko Thank you!! I corrected my question; one should consider the $l$-adic completion of the limit in question. About your second remark: surely, the image of Gysin could kill a part of the cohomology of $X$; yet my idea was to prove that for any 'small enough' $X_i$ its cohomology injects into the one of $\eta$.
Mar 24, 2014 at 18:12 vote accept Mikhail Bondarko
Mar 24, 2014 at 18:29
Mar 24, 2014 at 16:38 history answered D.-C. Cisinski CC BY-SA 3.0