Timeline for restriction of the cotangent bundle of an elliptic surface
Current License: CC BY-SA 3.0
10 events
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| Nov 30, 2012 at 13:24 | vote | accept | gummi | ||
| Nov 28, 2012 at 17:31 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Nov 28, 2012 at 1:03 | comment | added | Sándor Kovács | I see. Thanks for the link. I edited the answer to reflect this issue. | |
| Nov 28, 2012 at 1:02 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Nov 27, 2012 at 23:28 | comment | added | Damian Rössler | Yes I am saying that the map of sheaves may vanish. See for instance the article of Voloch, "On the conjectures of Mordell and Lang in positive characteristics" Invent. Math. 104, Lemma 1. The map is zero if and only if the curve can be defined over a smaller field, such that the corresponding field extension is purely inseparable. | |
| Nov 27, 2012 at 17:57 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Nov 27, 2012 at 17:53 | comment | added | Sándor Kovács |
Damian, I am not talking about the Kodaira-Spencer class in $H^1(X_t,T_{X_t})$, but the map of sheaves. That Kodaira-Spencer class could be zero even in characteristic zero. Are you saying that the map of sheaves $T_{\mathbb P^1}\to R^1f_*T_{X/\mathbb P^1}$ is zero?
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| Nov 27, 2012 at 8:23 | comment | added | Damian Rössler | The Kodaira-Spencer class may vanish if the base-field has positive characteristic. For instance, the pull-back by the absolute Frobenius of any elliptic fibration has a vanishing Kodaira-Spencer class. | |
| Nov 27, 2012 at 5:47 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Nov 27, 2012 at 5:35 | history | answered | Sándor Kovács | CC BY-SA 3.0 |