Timeline for Smoothness of $A \to A[T]/(h)$

9 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Sep 9, 2015 at 2:02	comment	added	user237522		Thank you very much (math.stackexchange.com/questions/1426025/…).
Sep 9, 2015 at 1:15	comment	added	Jason Starr		No, that claim is not true. You should read about the "Jacobian criterion". This is discussed in many basic algebraic geometry textbooks.
Sep 9, 2015 at 0:20	comment	added	user237522		@JasonStarr, please, is the claim I have suggested in the "Edit" true? I guess after your above comment that should be clear; however, I am not able to either prove or disprove it.
Sep 6, 2015 at 22:41	comment	added	user237522		@JasonStarr, please just to be sure we are working with the same definitions: $B$ is a smooth $A$-algebra if the following condition is satisfied: For each $A$-algebra $C$, and each ideal $J$ in $C$ with $J^2=0$, the canonical homomorphism $Hom_{A-alg}(B,C) \to Hom_{A-alg}(B,C/J)$ is surjective.
Sep 6, 2015 at 22:26	history	edited	user237522	CC BY-SA 3.0	added 264 characters in body
Sep 6, 2015 at 16:20	comment	added	user237522		Thank you very much! You can write it as an answer if you like.
Sep 6, 2015 at 14:47	comment	added	Jason Starr		The extension is formally smooth if and only if either $h$ is identically zero or $h(T)$ and $h'(T)$ generate the unit ideal of $A[T]$. You should look up "Jacobian criterion".
Sep 6, 2015 at 13:56	history	asked	user237522	CC BY-SA 3.0