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Dynamique analytique sur $\mathbf{Z}$. I : Mesures d'\'equilibre sur une droite projective relative
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Consider a Berkovich space over a good Banach ring and the relative projective line over it. (It is a space whose fibers are projective lines over different complete valued fields.) For each polarized endomorphism of this line, we prove that the family of equilibrium measures associated to the restrictions of the endomorphism to the fibers is continuous. The result holds, in particular, when the Banach ring is a complete valued field, a hybrid field, a complete discrete valuation ring, or the ring of integers of a number field.
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Cited by 2 Pith papers
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Explicit bounds on common projective torsion points of elliptic curves
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Global pluripotential theory for adelic line bundles
The category of strongly semiample adelic line bundles on a quasi-projective arithmetic variety is equivalent to line bundles on its Berkovich analytification with norm-equivariant continuous semipositive metrics.
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