Timeline for Intuition behind Artin/Grothendieck's Riemann existence theorem
Current License: CC BY-SA 3.0
3 events
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| Nov 14, 2016 at 1:34 | comment | added | nfdc23 | Typo: I meant to write "$z = 1/(\pi n)$ for $n \in \mathbf{Z} - \{0\}$" above. | |
| Nov 13, 2016 at 23:23 | comment | added | nfdc23 | The result you state (without precise reference) is false: you omitted a crucial etaleness hypothesis! Indeed, Remark 5.5 in Exp. XII gives a counterexample without that condition: let $X = \mathbf{A}^1 - \{0\}$ with coordinate $z$, and $\mathfrak{X}' \rightarrow X_h$ be the cover defined by $T^2 = \sin(1/z)$. The non-etale locus for this finite morphism is the infinite set of points $z = 1/(\pi n)$ for $n \in \mathbf{Z}$, so this cannot be the analytification of a finite map $Y \rightarrow X$, as the formation of the non-etale locus in the base is compatible with analytification. | |
| Nov 13, 2016 at 23:06 | history | asked | user388407 | CC BY-SA 3.0 |