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Kawaguchi–Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism

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We prove Kawaguchi–Silverman conjecture for all surjective endomorphisms on every smooth rationally connected variety admitting an int-amplified endomorphism.

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The authors would like to thank the organizers of “Younger generations in Algebraic and Complex geometry VI” where this collaboration started. The first author would like to thank Sheng Meng and De-Qi Zhang for stimulating discussions. The first author is supported by JSPS Research Fellowship for Young Scientists and KAKENHI Grant Number 18J11260. The second author is supported by the Program for Leading Graduate Schools, MEXT, Japan.

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Correspondence to Yohsuke Matsuzawa.

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Communicated by Vasudevan Srinivas.

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Matsuzawa, Y., Yoshikawa, S. Kawaguchi–Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism. Math. Ann. 382, 1681–1704 (2022).

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