Timeline for Confusion with the field of definition of a variety [closed]
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15, 2014 at 17:00 | history | closed |
Michael Zieve Stefan Kohl♦ abx Neil Strickland Piotr Achinger |
Not suitable for this site | |
| May 15, 2014 at 14:46 | comment | added | bananastack | @abx: I think it depends on how you define a subscheme. Whenever there is a sheaf $I$ with an injective map $I \to O_X$, I'd like to think of it as an ideal sheaf, regardless of whether it is in fact set-theoretically a subsheaf of $O_X$. If you used the functor of points approach, you might say that a subscheme is a special type of subfunctor, but I'm not sure there is much to gain from that point of view. In the end, isn't it just better to define a subscheme as some $Y$ together with an embedding into $X$? | |
| May 15, 2014 at 9:15 | comment | added | Dubious | @abx Yes you are right, this is the point. Two schemes $Y$ and $Y'$ are equal as subschemes of $X$ if they are isomorphic and this isomorphism commutes with two embeddings in $X$ | |
| May 15, 2014 at 8:55 | comment | added | abx | Two subschemes of a given scheme may, or may not, be equal; "isomorphic subschemes" does not make much sense. | |
| May 15, 2014 at 8:36 | review | Close votes | |||
| May 15, 2014 at 14:42 | |||||
| May 15, 2014 at 7:56 | comment | added | Jérôme Poineau | To understand what can go wrong, consider the case of a complex non-real line inside the complex plane. | |
| May 15, 2014 at 7:51 | answer | added | bananastack | timeline score: 1 | |
| May 15, 2014 at 7:41 | history | edited | Dubious | CC BY-SA 3.0 |
added 5 characters in body
|
| May 15, 2014 at 7:31 | history | edited | Dubious | CC BY-SA 3.0 |
deleted 1 character in body
|
| May 15, 2014 at 7:23 | history | asked | Dubious | CC BY-SA 3.0 |