A $1$-cohomologically hyperbolic birational map of $\mathbb{P}^3$, with a transcendental arithmetic degree

Abstract

We construct a $1$-cohomologically hyperbolic birational map of $\mathbb{P}^3$, with transcendental first dynamical degree. The arithmetic degree of this map at a $\overline{\mathbb{Q}}$-point is transcendental.