Timeline for Forms of algebraic varieties
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 1, 2014 at 23:22 | answer | added | Joe Silverman | timeline score: 6 | |
| Mar 1, 2014 at 21:28 | comment | added | ACL | Note, however, that without quasiprojectivity hypothesis, there may exist classes in $H^1$ which are not of this form. More precisely, given a (separated, of finite type) $L$-scheme $Y$ and a cocycle of $\mathop{\mathrm{Gal}}(L/K)$ with values in $\mathop{\mathrm{Aut}}(Y)$, there exists an algebraic space $X$ such that $X_L$ is isomorphic to $Y$, giving rise to the given cocycle. Mathieu Huruguen has given explicit examples of (non-quasiprojective) toric varieties $Y$ for which this phenomenon happens. | |
| Mar 1, 2014 at 15:55 | comment | added | Jonathan Beardsley | More generally, such "forms" of $Y$ are classified by this cohomology group for any morphism which is of effective descent. I think Waterhouse's "An Introduction to Affine Group Schemes" is really helpful. | |
| Mar 1, 2014 at 13:53 | vote | accept | Jérémy Blanc | ||
| Mar 1, 2014 at 13:44 | answer | added | jmc | timeline score: 6 | |
| Mar 1, 2014 at 13:29 | history | edited | Ben McKay | CC BY-SA 3.0 |
improved formatting
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| Mar 1, 2014 at 13:15 | comment | added | abx | Indeed: this is exactly Chapter III, 1.3, Proposition 5. | |
| Mar 1, 2014 at 13:08 | comment | added | user19475 | I think this can be found in Serre, Galois Cohomology. books.google.de/… p. 121, Section Forms | |
| Mar 1, 2014 at 12:56 | history | asked | Jérémy Blanc | CC BY-SA 3.0 |