Timeline for Fontaine-Fargues curve and period rings and untilt

7 events

when toggle format	what		by	license	comment
Jul 7, 2019 at 13:23	vote	accept	CommunityBot
Jul 7, 2019 at 6:57	answer	added	Filippo Alberto Edoardo		timeline score: 2
Jul 7, 2019 at 4:22	history	edited	user141691	CC BY-SA 4.0	added 197 characters in body
Jul 6, 2019 at 17:32	comment	added	Daniel Litt		$C$ is a choice of untilt!
Jul 6, 2019 at 15:54	comment	added	user141691		@DanielLitt Thanks for your answer. The map $\theta$ is defined the natural extension of $W(R)\rightarrow O_C:(x_0,x_1,...,x_n,...)\rightarrow \sum p^nx_n^{(n)}$ where $x_n=(x_n^{(m)})$ and $x_n^{(m)}\in O_C$. And $A_{cris}^0\subseteq W(R)[\frac{1}{p}]\subseteq B_{dR}^+\subseteq B_{dR}$. The untilt of a perfectoid field $K$ is a pair $(L,r)$, where $L$ is a perfectoid field and $r:L^b\cong K$ is an isomorphism. But I still can't see why $\theta$ determines such a pair $(L,r)$.
Jul 6, 2019 at 15:07	comment	added	Daniel Litt		Doesn't the map $\theta$ (and hence $\xi$) depend on a choice of untilt? Also, I think $A^0_{cris}$ should be a subring of $B_{dR}$, not $W(R)[1/p]$, right?
Jul 6, 2019 at 12:54	history	asked	user141691	CC BY-SA 4.0