Timeline for What is Mumford's example of a normal complex algebraic surface $X$ with non-torsion elements in $H^2_{et}(X,\mathbb{G}_m)$?
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| Feb 13, 2017 at 11:20 | comment | added | Martin Bright | The reference in Dix Exposés is: D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publications Math. 9 (1961), 5–22. | |
| Feb 13, 2017 at 8:30 | comment | added | Martin Bright | I don't remember a reference for Mumford's example, but I do remember approximately how it works. If you have a cone over, say, a plane cubic curve, then the local Weil divisor class group at the vertex has plenty of non-torsion elements. Now find a surface $X$ with a singularity that is étale locally isomorphic to that, but not Zariski locally, where your non-torsion class doesn't extend to a Weil divisor on a Zariski neighbourhood. To see where your Brauer class comes from, let $Y \to X$ be a resolution and look at the Leray spectral sequence for cohomology with values in $\mathbf{G}_m$. | |
| Feb 13, 2017 at 4:28 | history | edited | user19475 |
edited tags
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| Feb 13, 2017 at 4:24 | answer | added | user19475 | timeline score: 4 | |
| S Feb 13, 2017 at 4:07 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Typo in title.
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| Feb 13, 2017 at 3:50 | review | Suggested edits | |||
| S Feb 13, 2017 at 4:07 | |||||
| Feb 12, 2017 at 21:38 | history | asked | Zhaoting Wei | CC BY-SA 3.0 |