17 citations · 55 across the 21 of their papers we have counts for
24 papers
On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties
Yohsuke Matsuzawa, Kaoru Sano
We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. A…
Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Yohsuke Matsuzawa
Consider a dominant rational self-map on a smooth projective variety defined over . We prove that \begin{align} \lim_{n \to \infty} \frac{h_{Y}(f^{n}…
Arithmetic degree and its application to Zariski dense orbit conjecture
Yohsuke Matsuzawa, Junyi Xie
We prove that for a dominant rational self-map on a quasi-projective variety defined over , there is a point whose -orbit is well-defined and its arit…
Existence of arithmetic degrees for generic orbits and dynamical Lang-Siegel problem
Yohsuke Matsuzawa
We prove the existence of the arithmetic degree for dominant rational self-maps at any point whose orbit is generic. As a corollary, we prove the same existence for étale morphisms…
Recent advances on Kawaguchi-Silverman conjecture
Yohsuke Matsuzawa
This is a survey on Kawaguchi-Silverman conjecture.
On preimages question
Yohsuke Matsuzawa, Kaoru Sano
For a surjective self-morphism on a projective variety defined over a number field, we study the preimages question, which asks if the set of rational points on the iterated preima…
Distribution of rational points on random Fano hypersurfaces
Yohsuke Matsuzawa, Yuta Suzuki
We prove an asymptotic formula for the average number of rational points on Fano hypersurfaces that are contained in a small ball centered at a given adelic point. We also prove an…
Arithmetic degrees and Zariski dense orbits of cohomologically hyperbolic maps
Yohsuke Matsuzawa, Long Wang
A dominant rational self-map on a projective variety is called -cohomologically hyperbolic if the -th dynamical degree is strictly larger than other dynamical degrees. For su…
On Dynamical Cancellation
Jason P. Bell, Yohsuke Matsuzawa, Matthew Satriano
Let be a projective variety and let be a dominant endomorphism of , both of which are defined over a number field . We consider a question of the second author, Meng,…
Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics
Yohsuke Matsuzawa
Assuming Vojta's conjecture, we give a sufficient condition for the limit \[ \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x))} \] is equal to zero, where $f \colon X \lon…
The Distribution Relation and Inverse Function Theorem in Arithmetic Geometry
Yohsuke Matsuzawa, Joseph H. Silverman
We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across…
Height functions associated with closed subschemes
Yohsuke Matsuzawa
This is an expository note on height functions associated with closed subschemes. This manuscript contains nothing new.
Invariant subvarieties with small dynamical degree
Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata +2
Let be a dominant self-morphism of an algebraic variety over an algebraically closed field of characteristic zero. We consider the set of -periodic…
Growth of local height functions along orbits of self-morphisms on projective varieties
Yohsuke Matsuzawa
In this paper, we consider the limit where is a surjective self-morphism on a…
A note on Kawaguchi-Silverman conjecture
Sichen Li, Yohsuke Matsuzawa
We collect some results on endomorphisms on projective varieties related with the Kawaguchi-Silverman conjecture. We discuss certain condition on automorphism groups of projective…
Non-density of points of small arithmetic degrees
Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata +1
Given a surjective endomorphism on a projective variety over a number field, one can define the arithmetic degree of at a point in . The Kawaguchi…
Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
Yohsuke Matsuzawa, Shou Yoshikawa
We prove Kawaguchi-Silverman conjecture for all surjective endomorphisms on every smooth rationally connected variety admitting an int-amplified endomorphism.
Int-amplified endomorphisms on normal projective surfaces
Yohsuke Matsuzawa, Shou Yoshikawa
We investigate int-amplified endomorphisms on normal projective surfaces. We prove that the output of the equivariant MMP is either a Q-abelian surface, a (equivariant) quasi-étale…
Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties
Yohsuke Matsuzawa
We prove Kawaguchi-Silverman conjecture (KSC) and Shibata's conjecture on ample canonical heights for endomorphisms on several classes of algebraic varieties including varieties of…
Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties
Yohsuke Matsuzawa, Kaoru Sano
We prove a conjecture by Kawaguchi-Silverman on arithmetic and dynamical degrees, for self-morphisms of semi-abelian varieties. Moreover, we determine the set of the arithmetic deg…
Arithmetic degrees for dynamical systems over function fields of characteristic zero
Yohsuke Matsuzawa, Kaoru Sano, Takahiro Shibata
We study arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We see that the notion of arithmetic degree…
Arithmetic degrees and dynamical degrees of endomorphisms on surfaces
Yohsuke Matsuzawa, Kaoru Sano, Takahiro Shibata
For a dominant rational self-map on a smooth projective variety defined over a number field, Kawaguchi and Silverman conjectured that the (first) dynamical degree is equal to the a…
On upper bounds of arithmetic degrees
Yohsuke Matsuzawa
Let be a smooth projective variety over , and be a dominant rational map. Let be the first dynamical degree of and $h_{X}…
Invariant Hilbert Schemes and Luna's Etale Slice Theorem
Yohsuke Matsuzawa
Luna's etale slice theorem is a useful theorem for the local study of quotients by reductive algebraic groups. In this article, we show that the slice theorem can also be used to s…