Higher arithmetic degrees of dominant rational selfmaps
Suppose that f : X > X is a dominant rational selfmap of a smooth projective variety defined over Q. Kawaguchi and Silverman conjectured that if P ∈ X(Q) is a point with welldefined forward orbit, then the growth rate of the height along the orbit exists, and coincides with the first dynamical degree λ_1(f) of f if the orbit of P is Zariski dense in X.
In this note, we extend the KawaguchiSilverman conjecture to the setting of orbits of higherdimensional subvarieties of X. We begin by defining a set of arithmetic degrees of f, independent of the choice of cycle, and we then develop the theory of arithmetic degrees in parallel to existing results for dynamical degrees. We formulate several conjectures governing these higher arithmetic degrees, relating them to dynamical degrees.
Higher arithmetic degrees of dominant rational selfmaps, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), Vol. XXIII (2022), 463481, https://doi.org/10.2422/20362145.201908_014.
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Work Title  Higher arithmetic degrees of dominant rational selfmaps 

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Publication Date  March 30, 2022 
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Deposited  August 26, 2022 
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