Papers

Expository notes and Surveys.

1. Height functions associated with closed subschemes , arXiv:2008.08153

2. Recent advances on Kawaguchi-Silverman conjecture, pdf.

3. 高次元数論力学系の諸問題(代数学シンポジウム2023の報告集), pdf.

Research papers 

1. On the Invariant Hilbert schemes and Luna’s etale slice theorem,  Manuscripta Math. 156 (2018), no. 3-4, 329--340.

2. On the Hilbert schemes of finite algebras over an algebraically closed field,  Comm. Algebra 46 (2018), no. 6, 2753--2765.

3. Arithmetic degree for dynamical systems over function fields of characteristic zero (with K. Sano and  T. Shibata), Math. Z. 290 (2018), no. 3-4, 1063--1083.

4. Arithmetic degrees and dynamical degrees of endomorphisms on surfaces (with K. Sano and  T. Shibata), Algebra Number Theory 12 (2018), no. 7, 1635--1657.

5. Y. Matsuzawa, T. Kataoka, 信号制御の最適化のための目的関数, 数理科学実践研究レター 2018.

6. T. Kataoka, Y. Matsuzawa, 局所最適な信号制御とその大域化, 数理科学実践研究レター 2018.

7.  Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties (with K. Sano), Ergod. Theory and Dyn. Sys., 40 (2020), no. 6, 1655–1672. 

8. On upper bounds of arithmetic degrees, Amer. J. Math., 142 (2020), no. 6, 1797–1820. 

9. Arithmetic and dynamical degrees of rational self-maps on algebraic varieties, to appear in RIMS Kokyuroku Bessatsu.

10. Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties, Adv. Math., 366 (2020), 107086, 26 pp. 

11. Int-amplified endomorphisms on normal projective surfaces (with Shou Yoshikawa), Taiwanese J. Math. 25 (2021), no. 4, 681–697.

12. Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism (with Shou Yoshikawa), Math. Ann. 382 (2022), no. 3-4, 1681--1704. arXiv:1908.11537

13. Non-density of points of small arithmetic degrees (with S. Meng, T. Shibata, and D.-Q. Zhang), J. Geom. Anal. 33 (2023), no. 4, Paper No. 112, 41 pp. arXiv:2002.10976

14. A note on  Kawaguchi-Silverman conjecture (with S. Li), Internat. J. Math. 32 (2021), no. 11, Paper No. 2150085, 12 pp.

15. Growth of local height functions along orbits of self-morphisms on projective varieties, Int. Math. Res. Not. IMRN (2023), no. 4, 3533--3575. arXiv:2005.08093

16. Invariant subvarieties with small dynamical degree (with S.Meng, T.Shibata, D.-Q. Zhang, and G. Zhong), Int. Math. Res. Not. IMRN (2022), no. 15, 11448--11483. arXiv:2005.13368

17. The Distribution Relation and Inverse Function Theorem in Arithmetic Geometry (with J. H. Silverman),  J. Number Theory, Volume 226, September 2021, Pages 307-357. arXiv:2008.08149

18. Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics, arXiv:2012.04693

19. On dynamical cancellation (with J.P. Bell and M. Satriano),  Int. Math. Res. Not. IMRN (2023), no. 8, 7099--7139. arXiv:2106.11544

20. Arithmetic degrees and Zariski dense orbits of cohomologically hyperbolic maps (with L. Wang), to appear in Trans. Amer. Math. Soc. arXiv:2212.05804

21. Distribution of rational points on random Fano hypersurfaces (with Y. Suzuki), arXiv:2310.13408

22. On preimages question (with K. Sano), arXiv:2311.02906