Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cremona groups over finite fields, Neretin groups, and non-positively
  curved cube complexes   We show that plane Cremona groups over finite fields embed into Neretin
groups, i.e., groups of almost automorphisms of rooted trees. The image of this
embedding is dense if our base field has odd characteristic or is equal to
$F_2$. This is no longer true, if the finite base field has even characteristic
and contains at least 4 elements; for this case we show that the permutations
induced by birational transformations on rational points of regular projective
surfaces are always even.
  In a second part, we construct explicit locally compact CAT(0) cube
complexes, on which Neretin groups act properly. This allows us to recover in a
unified way various results on Neretin groups such as that they are of type
$F_{\infty}$. We also prove a new fixed-point theorem for CAT(0) cube complexes
without infinite cubes and use it to deduce a regularisation theorem for plane
Cremona groups over finite fields.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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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: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org