Timeline for Existence of an open dense of a connected scheme such that the preimage under a surjective finite etale map is connected
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| Nov 10, 2019 at 4:58 | comment | added | R. van Dobben de Bruyn | This is automatic if $X$ is normal (or more generally geometrically unibranch), for then so is $Y$, so any open in $X$ or $Y$ is irreducible if and only if it is connected, and a nonempty open in an irreducible is irreducible. To see that it fails already for nodal curves, look at Figure 12 in Exercise III.10.6 in Hartshorne (take $U$ the complement of the node). | |
| Nov 10, 2019 at 4:50 | review | First posts | |||
| Nov 10, 2019 at 7:03 | |||||
| Nov 10, 2019 at 4:48 | history | asked | user148385 | CC BY-SA 4.0 |