Timeline for Top chern class under finite, unramified, dominant morphism
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2013 at 12:00 | comment | added | Ariyan Javanpeykar | @Jesko. I corrected the last formula for the compactly supported Euler characteristic. I had made a slight mistake in calculating the Euler characteristic of $\pi^{-1}(D-D^{sing})$. This is not equal to $\deg \pi e_c(D-D^{sing})$. | |
| Jan 29, 2013 at 11:58 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
Corrected the last formula
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| Jan 23, 2013 at 21:56 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
deleted 7 characters in body
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| Jan 23, 2013 at 10:43 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Jan 23, 2013 at 9:53 | comment | added | Ariyan Javanpeykar | I'm glad the answer is useful. I added another result which describes the error term more precisely (under some mild hypotheses on $\pi:Y\to X$); see (4) in the last theorem. One of the hypotheses is that the branch locus of $\pi:Y\to X$ is a strict normal crossings divisor. Note that this can always be achieved by Hironaka's theorem (embedded resolution of singularities); see page 404-407 of Liu's book (Section 9.2.4 and the remark right after Remark 2.36). Let me know if anything seems obscure (there are certainly some details missing in the proof of the last statement). | |
| Jan 23, 2013 at 9:48 | comment | added | Ariyan Javanpeykar | I'm pretty sure Mayer-Vietoris also holds in etale cohomology. I don't know of a precise reference, though. But it should be somewhere in Milne's notes on etale cohomology. | |
| Jan 23, 2013 at 9:47 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
Added a theorem describing the error term even more precisely
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| Jan 22, 2013 at 17:58 | comment | added | Jesko Hüttenhain | PS: I ask because that corollary is, in fact, of serious interest to me =). | |
| Jan 22, 2013 at 17:57 | comment | added | Jesko Hüttenhain | First of all, +1 and thanks for the very detailed Answer. I only know Mayer-Vietoris for singular Homology, is there an equivalent for the $\ell$-adic one? | |
| Jan 22, 2013 at 9:21 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Jan 21, 2013 at 14:00 | history | answered | Ariyan Javanpeykar | CC BY-SA 3.0 |