Timeline for Pushforward of semi-stable sheaves under finite field extension
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 21, 2017 at 10:56 | vote | accept | user43198 | ||
| Aug 21, 2017 at 10:54 | comment | added | R. van Dobben de Bruyn | @user43198: the pushforward will not have the same Hilbert polynomial. Its rank is multiplied by $[\ell:k]$ under pushforward. | |
| Aug 21, 2017 at 5:22 | comment | added | user43198 | Doesn't this imply that a non-empty moduli space $M_X(P)$ parametrizing semi-stable sheaves on $X$ with Hilbert polynomial $P$, will always have a $k$-rational point? In particular, if I understand correctly, the moduli space being non-empty implies that there exists a finite extension $L$ of $k$ such that there exists a semi-stable sheaf $E$ on $X_L$ with Hilbert polynomial $P$. Then, by your argument, we have that $p_∗E$ is semi-stable on $X$, which will give a $k$-rational point of $M_X(P)$. Am I missing something? | |
| Aug 20, 2017 at 17:54 | vote | accept | user43198 | ||
| Aug 20, 2017 at 17:54 | |||||
| Aug 18, 2017 at 17:32 | history | answered | R. van Dobben de Bruyn | CC BY-SA 3.0 |