Homomorphisms of Abelian Varieties
نویسنده
چکیده
Throughout the paper we will freely use the following observation [21, p. 174]: if an abelian variety X is isogenous to a self-product Z of an abelian variety Z then a choice of an isogeny between X and Z defines an isomorphism between End(X) and the algebra Md(End (Z)) of d× d matrices over End(Z). Since the center of End(Z) coincides with the center of Md(End (Z)), we get an isomorphism between the center of End(X) and the center of End(Z) (that does not depend on the choice of an isogeny). Also dim(X) = d · dim(Z); in particular, both d and dim(Z) divide dim(X).
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