Error on 1
{ [“2”] = exit,[“3”] = 1,} \documentclass{standalone} \input{/home/zack/.pandoc/custom/preamble_common} \begin{document} \nopagecolor \begin{tikzcd} {\in \Algs{R}} &&&&&& {\in {\mathsf{Sch}}_{/ {S}} } \ \textcolor{rgb,255:red,92;green,92;blue,214}{R} && {\forall B} && {\forall T} && \textcolor{rgb,255:red,92;green,92;blue,214}{X} \ \ \textcolor{rgb,255:red,92;green,92;blue,214}{A} && {\forall B/I,\quad I^2=0} && {T_1 {\scriptsyle \text{first order thickening}}} && \textcolor{rgb,255:red,92;green,92;blue,214}{S} \ {} &&&& {} \arrow[draw={rgb,255:red,92;green,92;blue,214}, from=2-1, to=4-1] \arrow[“\forall”, from=2-1, to=2-3] \arrow[““{name=0, anchor=center, inner sep=0}, two heads, from=2-3, to=4-3] \arrow[“{\forall }”, from=4-1, to=4-3] \arrow[“{\exists \leq 1}”{description}, dashed, from=4-1, to=2-3] \arrow[from=4-5, to=4-7] \arrow[draw={rgb,255:red,92;green,92;blue,214}, from=2-7, to=4-7] \arrow[from=2-5, to=2-7] \arrow[””{name=1, anchor=center, inner sep=0}, “{\forall }”, from=2-5, to=4-5] \arrow[“{\exists !}”{description}, dashed, from=4-5, to=2-7] \arrow[shorten <=26pt, shorten >=26pt, Rightarrow, squiggly, from=0, to=1] \end{tikzcd} \end{document}
aliases:
- formally unramified date: “2022-03-23 12:43” modification date: “Wednesday 23rd March 2022 12:43:03” title: formally unramified
Last modified date: <%+ tp.file.last_modified_date() %>
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- scheme
- formally smooth
- formally etale
formally unramified
Idea: meant to look like an immersion.
Similar to formally etale, except at most one extension should exist:
TFAE:
- \(f\in {\mathsf{Sch}}(X, S)\) is formally unramified
- \(\Omega_{X/S} = 0\) (i.e. the relative differentials vanish).
- \({{\Gamma}\qty{X; {\mathcal{O}}_X} }\to {{\Gamma}\qty{Y; {\mathcal{O}}_Y} }\) is a formally unramified morphism of rings.