Timeline for Does there exist a discrete valuation subring $R$ of $K((t))$ ($K$ a number field) of residue characteristic $p$ with $\mathrm{Frac}(R) = K((t))$?

6 events

when toggle format	what		by	license	comment
Feb 7, 2019 at 18:35	vote	accept	Will Chen
Feb 7, 2019 at 16:31	answer	added	Will Sawin		timeline score: 13
Feb 7, 2019 at 11:58	comment	added	Jason Starr		Let $L=K(\{s_i:i\in I\})$ be a maximal purely transcendental subextension of $K((t))/K$. Denote the integer ring of $K$ by $\mathfrak{o}_K$, and let $\mathfrak{p}$ be an ideal over $p\mathbb{Z}$. For the infinite polynomial ring $S=\mathfrak{o}_K[\{s_i:i\in I\}]$, the ideal $\mathfrak{p}S$ is a height one prime. The localization $S_{\mathfrak{p}S}$ is a DVR. For the algebraic field extension $K((t))/L$, there is a valuation ring $R$ dominating $S_{\mathfrak{p}S}$ whose fraction field equals $K((t))$. By Krull-Akizuki, you can choose $R$ to be a colimit of DVRs, probably not a DVR itself.
S Feb 7, 2019 at 10:07	history	suggested	user26857	CC BY-SA 4.0	improving format
Feb 7, 2019 at 9:35	review	Suggested edits
S Feb 7, 2019 at 10:07
Feb 6, 2019 at 6:55	history	asked	Will Chen	CC BY-SA 4.0