Geodesic
Abelian absolute Galois groups
Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 359-367

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DOI

Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if $K$ is a finitely generated extension of transcendence degree $r$ of a global field and $A$ is a closed abelian subgroup of $\textrm{Gal}(K)$, then ${\mathrm{rank}}(A)\le r+1$. Moreover, if $\mathrm{char}(K)=0$, then ${\hat{\mathbb{Z}}}^{r+1}$ is isomorphic to a closed subgroup of $\textrm{Gal}(K)$.
DOI : 10.1017/S0017089524000028
Mots-clés : Absolute Galois Group, Henselian Fields 
Jarden, Moshe. Abelian absolute Galois groups. Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 359-367. doi: 10.1017/S0017089524000028
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     title = {Abelian absolute {Galois} groups},
     journal = {Glasgow mathematical journal},
     pages = {359--367},
     year = {2024},
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     doi = {10.1017/S0017089524000028},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000028/}
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