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Dec 27, 2014 at 19:57 comment added Roman Fedorov But already if you replace the line with a punctured elliptic curve, the statement is no longer true: every analytic torsor is trivial, while a $\mathbb{G}_m$-torsor may be algebraically non-trivial.
S Dec 27, 2014 at 16:46 history answered Jason Starr CC BY-SA 3.0
S Dec 27, 2014 at 16:46 history made wiki Post Made Community Wiki by Jason Starr