Timeline for Good and bad reduction for twists of algebraic curves
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2023 at 12:41 | comment | added | Ariyan Javanpeykar | A bit more explanation: When we say that a field extension $K/\mathbb{Q}_p$ is unramified, we really mean that $\mathbb{Z}_p\subset O_K$ is unramified. But $O_K$ is the normalization (read: integral closure) of $\mathbb{Z}_p$ in $K$. | |
| Jul 26, 2023 at 12:41 | comment | added | Ariyan Javanpeykar | @did you're welcome. By definition, by $L/K$ being unramified, I really just meant that the normalization of $B$ in $L$ is unramified. But the normalization $B'\to B$ is a finite surjective morphism and if it is unramified, then it is in fact etale (by normality of $B$). I can highly recommend Liu's book on Arithmetic Geometry. | |
| S Jul 26, 2023 at 12:32 | history | suggested | did | CC BY-SA 4.0 |
small typo correction
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| Jul 26, 2023 at 11:29 | comment | added | did | Thank you @Ariyan! I just wanted to ask why $L/K$ being unramified implies that $B'$ is finite flat etale over $B$ and do you have a good reference for these notions? | |
| Jul 26, 2023 at 11:27 | vote | accept | did | ||
| Jul 26, 2023 at 11:27 | review | Suggested edits | |||
| S Jul 26, 2023 at 12:32 | |||||
| Jul 26, 2023 at 7:20 | history | answered | Ariyan Javanpeykar | CC BY-SA 4.0 |