Timeline for When does 'Zariski tangent space derivative' vanishes everywhere imply that a section is constant?

9 events

when toggle format	what		by	license	comment
Dec 10, 2015 at 7:39	answer	added	Qiaochu Yuan		timeline score: 4
Dec 9, 2015 at 22:03	comment	added	James E Hanson		There was no $K$ in the question when მამუკა ჯიბლაძე responded.
Dec 9, 2015 at 21:46	comment	added	Julian Rosen		@მამუკაჯიბლაძე There is a canonical choice of splitting map $R/m\to R/m^2$, which identifies $R/m$ with $K$ then includes into $R/m^2$ by the structure map (the map making $R/m^2$ into a $K$-algebra).
Dec 9, 2015 at 21:12	history	edited	James E Hanson	CC BY-SA 3.0	Restricted to K-algebra case to make the problem well-posed.
Dec 9, 2015 at 21:07	comment	added	James E Hanson		Yes that's true. I'll edit the question to make it more specific.
Dec 9, 2015 at 20:36	history	edited	Leo Alonso		edited tags
Dec 9, 2015 at 20:33	comment	added	მამუკა ჯიბლაძე		Does not the answer depend on the choice of an isomorphism $R/m^2\cong R/m\oplus m/m^2$? I don't see any canonical map which one might require to be an isomorphism. There are maps $m/m^2\to R/m^2\to R/m$, one may require this to be a split short exact sequence, but a choice of the splitting still has to be made, and I think the answer will depend on it.
Dec 9, 2015 at 20:02	review	First posts
Dec 9, 2015 at 20:03
Dec 9, 2015 at 19:58	history	asked	James E Hanson	CC BY-SA 3.0