Timeline for Killing cohomology of structure sheaf by pullback along Frobenius and finite etale covers
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2021 at 17:04 | comment | added | LSpice | Name of the linked paper (referenced for "Prop 2.3"): Brenner and Kaid - On deep Frobenius descent and flat bundles. @ali's reference: Hochster and Huneke - Absolute integral closures are big Cohen–Macaulay algebras in characteristic $P$. | |
| Jan 24, 2021 at 3:36 | comment | added | R. van Dobben de Bruyn | This has little to do with whether $i$ equals $\dim X$, as you can take a product of any of these with $\mathbf P^N$. I think that already gives counterexamples for each $i \geq 2$ in each dimension $d \geq i$. | |
| Jan 24, 2021 at 3:03 | history | edited | user127776 | CC BY-SA 4.0 |
added 7 characters in body
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| Jan 24, 2021 at 3:03 | comment | added | user127776 | I see so $i=dim(X)$ is problematic. | |
| Jan 23, 2021 at 17:30 | comment | added | Anonymous | Take an ordinary smooth projective Calabi-Yau hypersurface $X \subset \mathbf{P}^{n+1}$ of big dimension (probably $n\geq 2$ is enough). Then $X$ will be simply connected as $n$ is big, so finite etale covers are useless. Ordinarity means the Frobenius acts bijectively on the $1$-dimensional vector space $H^n(X,\mathcal{O}_X)$, so that doesn't help either. | |
| Jan 23, 2021 at 10:02 | comment | added | user127776 | This seems like an expository paper. I'm not sure whether by finite and surjective they mean what I mean. I specifically require it to be a composition of Frobenius and finite etale covers. | |
| Jan 23, 2021 at 6:47 | comment | added | ali | yes you can. look at the paper of Hochster and Huneke for a generalisation: projecteuclid.org/download/pdf_1/euclid.bams/1183556250 | |
| Jan 23, 2021 at 5:54 | history | asked | user127776 | CC BY-SA 4.0 |