Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The canonical heights for Jordan blocks of small eigenvalues,
  preperiodic points, and the arithmetic degrees   We introduce a new canonical height function for Jordan blocks of small
eigenvalues for endomorphisms on smooth projective varieties over a number
field. We prove that under an assumption on the eigenvalues of the endomorphism
on the group of divisors modulo numerical equivalence, the arithmetic degree at
a rational point is equal to one if and only if it is preperiodic under the
endomorphism.

28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th