Serre’s generalization of Nagao’s theorem: an elementary approach. (English) Zbl 0964.20027
Let \(C\) be the coordinate ring of the affine curve obtained by removing a closed point from a smooth projective curve over a field. Serre has proved that \(\text{GL}_2(C)\) is isomorphic to the fundamental group of a graph of groups. In the paper, a more elementary and explicit proof is given.
MSC:
| 20H25 | Other matrix groups over rings |
| 14H05 | Algebraic functions and function fields in algebraic geometry |
| 20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |
References:
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