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Xiao Zhong
Preimages question for surjective endomorphisms on (P1)n
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| Published: |
March 31, 2025. |
| Keywords: |
Preimages Question, invariant subvarieties, arithmetic dynamics, rational points on varieties. |
| Subject [2020]: |
37P55, 14G05. |
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Abstract
Let K be a number field and let f : (P1)n -->
(P1)n be a dominant endomorphism defined over K. We show that
if V is an f-invariant subvariety (that is, f(V)=V) then there is a positive integer
s0 such that (f-s-1(V) \ f-s(V))(K) is empty for
every integer s greater than or equal to s0, answering the Preimages
Question of Matsuzawa, Meng, Shibata, and Zhang in the case of (P1)n.
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| Acknowledgements
The author was supported in part by NSERC grant RGPIN-2022-02951.
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| Author information
Xiao Zhong
University of Waterloo
Department of Pure Mathematics
Waterloo, Ontario N2L 3G1, Canada
x48zhong@uwaterloo.ca
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