Timeline for What is the arithmetic fundamental group?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Aug 17, 2016 at 0:32 | comment | added | nfdc23 | For a geometrically connected scheme $X$ of finite type over a field $k$, it is convenient to have distinct names for $\pi_1(X)$ and $\pi_1(X_{k_s})$ (linked through the exact sequence $1 \rightarrow \pi_1(X_{k_s}) \rightarrow \pi_1(X) \rightarrow {\rm{Gal}}(k_s/k) \rightarrow 1$). The latter is called the "geometric fundamental group" (since it coincides with $\pi_1(X_{\overline{k}})$), and the former is called the "arithmetic fundamental group". It would be entirely logical to drop the word "arithmetic", and it is fine to do so. But the convention persists, for emphasis I suppose. | |
| Aug 17, 2016 at 0:24 | answer | added | Will Chen | timeline score: 16 | |
| Aug 17, 2016 at 0:02 | history | asked | user97187 | CC BY-SA 3.0 |