Timeline for Etale Realization and Gysin Sequence
Current License: CC BY-SA 3.0
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| Dec 10, 2014 at 16:05 | comment | added | Mikhail Bondarko | This is definitely true for the paper your cite. Yet I believe that the statement you want can be extracted from other papers of Deglise. The alternative author is Ayoub (but I have never read much of him). | |
| Dec 10, 2014 at 14:36 | comment | added | Grilo | Thanks for the answer. But I am still confused. Deglise's papers shows the naturality of the Gysin triangle (Prop. 2.3 in arxiv.org/pdf/0804.2415.pdf). What I want to learn is that if I construct a natural map from Motivic cohomology (or homology) to etale cohomology using above realization, is the two localization sequences of the pair $(X,Z)$, where $Z$ smooth closed subscheme of $X$ of pure codimension, in both motivic (co)homology and etale cohomology fit in a commutative diagram. | |
| Dec 4, 2014 at 21:31 | history | answered | Mikhail Bondarko | CC BY-SA 3.0 |