Density of Orbits of Endomorphisms of Connected Commutative Linear Algebraic Groups
نویسنده
چکیده
We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups G defined over an algebraically closed field k of characteristic 0. That is, if Φ: G −→ G is a dominant endomorphism, we prove that one of the following holds: either there exists a non-constant rational function f ∈ k(G) preserved by Φ (i.e., f ◦ Φ = f), or there exists a point x ∈ G(k) whose Φ-orbit is Zariski dense in G.
منابع مشابه
Density of orbits of endomorphisms of commutative linear algebraic groups
We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups G defined over an algebraically closed field k of characteristic 0. That is, if Φ: G −→ G is a dominant endomorphism, we prove that one of the following holds: either there exists a non-constant rational function f ∈ k(G) preserved by Φ (i.e., f ◦ Φ = f), or there exists a point x ∈ ...
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تاریخ انتشار 2017