Timeline for Real algebraic variety and real algebraic bundle
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2010 at 12:35 | vote | accept | Yashica | ||
| Aug 4, 2010 at 17:36 | answer | added | Richard Borcherds | timeline score: 3 | |
| Aug 4, 2010 at 11:28 | comment | added | BCnrd | As an illustration of Torsten's parenthetical remark, on p. 210 of the book "Neron models" there's a nice example (due to Mumford) of a scheme loc. of finite type over $\mathbf{C}[[t]]$ equipped with descent data relative to $\mathbf{R}[[t]]$ so that the descent is an algebraic space and not a scheme. The same example works using $\mathbf{C}[t]$ and $\mathbf{R}[t]$, so it provides schemes of finite type over $\mathbf{C}$ which descend to non-scheme alg. spaces over $\mathbf{R}$. Unless one assumes $X$ is q-projective, it seems hard to determine when the descent as an alg. space is a scheme. | |
| Aug 4, 2010 at 7:54 | comment | added | Torsten Ekedahl | You need a semi-linear $\sigma$, i.e., it covers complex conjugation on $\mathbb C$. In that case the $\mathbb R$-scheme is obtained by descent theory as the quotient by $X$ under $\sigma$ (though I guess in general this quotient will only be an algebraic space). | |
| Aug 4, 2010 at 6:24 | history | edited | Charles Matthews | CC BY-SA 2.5 |
my typo
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| Aug 4, 2010 at 5:13 | history | asked | Yashica | CC BY-SA 2.5 |