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Jul 8, 2019 at 16:38 comment added user141691 Thank you very much !
Jul 8, 2019 at 16:12 comment added Filippo Alberto Edoardo Yea, especially in the isomorphism $\mathrm{Pic}(X)\cong\mathbb{Z}$.
Jul 7, 2019 at 13:45 comment added user141691 Thanks for your detailed answer. When I study p-adic Hodge, I haven't thought that we can replace $C_p$ with other complete algebraic closed non-archimedean field in the constructions of these period rings. One more question: Does the construction in (6) you mentioned mean the two hypotheses $Pic(X)\cong Z$ and $H^1(X,O_X(k))=0$ for all $k\geq0$ on page 11?
Jul 7, 2019 at 13:23 vote accept CommunityBot
Jul 7, 2019 at 6:57 history answered Filippo Alberto Edoardo CC BY-SA 4.0