Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical canonical heights for Jordan blocks, arithmetic degrees of
  orbits, and nef canonical heights on abelian varieties   Let f : X --> X be an endomorphism of a normal projective variety defined
over a global field K, and let D_0,D_1,D_2,... be divisor classes that form a
Jordan block with eigenvalue b for the action of f^* on Pic(X) tensored with C.
We construct appropriately normalized canonical heights h_0,h_1,h_2,...
associated to D_0,D_1,D_2,... and satisfying Jordan transformation formulas
h_k(f(x)) = b h_k(x) + h_{k-1}(x). As an application, we prove that for every x
in X, the arithmetic degree a_f(x) exists, is an algebraic integer, and takes
on only finitely many values as x varies over X. Further, if X is an abelian
variety defined over a number field and D is a nonzero nef divisor, we
characterize points satisfying h_D(x)=0, and we use this characterization to
prove that if the f-orbit of x is Zariski dense in X, then a_f(x) is equal to
the dynamical degree of f.

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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat