Timeline for Absoluteness of motivic cohomology and restriction of scalars
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2018 at 17:30 | comment | added | Mikhail Bondarko | You just consider certain closed subschemes in $(\mathbb{P}^1)^n(X)$ (or something similar). They are subvarieties automatically. | |
| Apr 12, 2018 at 17:25 | comment | added | Wenzhe | @MikhailBondarko But the definition of algebraic simplex $\Delta_n$ involves the base field, and also in the definition of complex, it makes use of algebraic subvarieties of $X \times \Delta_n$, which also involves the base field, how to see Bloch's definition actually is independent of the base field? | |
| Apr 12, 2018 at 17:05 | comment | added | Mikhail Bondarko | I don't think that Bloch's definition actually depends on the base field.:) | |
| Apr 12, 2018 at 10:24 | comment | added | François Brunault | See Poonen's book "Rational points on varieties" section 4.6. Also see the book "Néron models" by Bosch-Lütkebommert-Raynaud for the proof that restriction of scalars preserve being smooth projective. The following MO discussion should also be useful mathoverflow.net/questions/212989/… | |
| Apr 12, 2018 at 9:25 | comment | added | Wenzhe | Could I bother you with a reference about the definition of restriction of scalars given by a functor and the theorem you have mentioned? | |
| Apr 12, 2018 at 9:22 | vote | accept | Wenzhe | ||
| Apr 12, 2018 at 9:12 | comment | added | François Brunault | I don't think looking at the composite $X \to \mathrm{Spec} F \to \mathrm{Spec} Q $ is the good notion of restriction of scalars. It is rather defined by a functor, and it is a theorem that for smooth projective varieties this functor is representable. As an example, restriction of scalars of an elliptic curve E/F is an abelian variety A/Q of dimension [F:Q]. | |
| Apr 12, 2018 at 9:07 | answer | added | François Brunault | timeline score: 1 | |
| Apr 11, 2018 at 21:30 | history | asked | Wenzhe | CC BY-SA 3.0 |