Galois embedding of algebraic variety and its application to abelian surface

We define a Galois embedding of a projective variety V and give a criterion whether an embedding is Galois or not. Then we consider several representations of the Galois group. Following the method developed in the first half, we consider the structure of an abelian surface with the Galois embedding in the latter half. We give a complete list of all possible groups and show that the abelian surface is isogenous to the square of an elliptic curve. 2000 Mathematics Subject Classification number: 14N10, 14J99, 14K9