Endomorphism Algebras of Abelian varieties with special reference to Superelliptic Jacobians

摘要

This is (mostly) a survey article. We use an information about Galoisproperties of points of small order on an abelian variety in order to describeits endomorphism algebra over an algebraic closure of the ground field. Wediscuss in detail applications to jacobians of cyclic covers of the projectiveline.