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Given a faithful action of a finite group on an algebraic curve of genus atleast 2, we prove that the induced action on the space of global holomorphicdifferentials is faithful as well, except in the following very special case:the given action is not tame, the genus of the quotient curve is 0 and thecharacteristic of the base field is 2.

Faithful action on the space of global differentials of an algebraic curve