Density of Orbits of Endomorphisms of Abelian Varieties
نویسنده
چکیده
Let A be an abelian variety defined over Q̄, and let φ be a dominant endomorphism of A as an algebraic variety. We prove that either there exists a non-constant rational fibration preserved by φ, or there exists a point x ∈ A(Q̄) whose φ-orbit is Zariski dense in A. This provides a positive answer for abelian varieties of a question raised by Medvedev and the second author in [MS14]. We prove also a stronger statement of this result in which φ is replaced by any commutative finitely generated monoid of dominant endomorphisms of A.
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