Timeline for Neron model: can number of components decrease after based change?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2014 at 13:19 | comment | added | Ariyan Javanpeykar | Minor nitpick: if you base-change the Neron model, then (obviously) the number of components can not decrease. What you are really asking is whether, for $X$ an abelian variety over $K$ (the function field of $R$, say) and $L/K$ finite field extension, the number of connected components of the Neron model of $X_L$ can be smaller than the number of connected components of the Neron model of $X$. As Kestutis Cesnavicius points out, this can happen unless you have semi-abelian reduction (as in the last part of your question). | |
| Jul 16, 2014 at 8:00 | vote | accept | Maxim | ||
| Jul 15, 2014 at 13:57 | answer | added | Kestutis Cesnavicius | timeline score: 8 | |
| Jul 15, 2014 at 13:30 | history | asked | Maxim | CC BY-SA 3.0 |