Endomorphism Algebras of Abelian varieties with special reference to Superelliptic Jacobians

2017/05/31 by Zarhin, Yuri G.
#11G30 #14H40 #14K05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.00110

Abstract

This is (mostly) a survey article. We use an information about Galois properties of points of small order on an abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line.

Related

• Homomorphisms of abelian varieties
• Endomorphism algebras of Jacobians of certain superelliptic curves
• Cyclic covers of prime power degree, jacobians and endomorphisms
• Endomorphism algebras of hyperelliptic jacobians and finite projective lines
• Endomorphisms of ordinary superelliptic jacobians