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arXiv · 1307.3205

Arithmetic dynamics on smooth cubic surfaces

Solomon Vishkautsan
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Abstract

We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We present results describing the sets of $K$ and $\bar{K}$-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity. Finally, we give a dynamical result relating to the Mordell--Weil problem on cubic surfaces.

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Solomon Vishkautsan. 2013-07-11. Arithmetic dynamics on smooth cubic surfaces. https://arxiv.org/abs/1307.3205

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