相关论文: Non-Archimedean Big Picard Theorems

In non-archimedean setting, we establish a Lehto--Virtanen-type theorem for a morphism from the punctured Berkovich closed unit disk $\overline{\mathsf{D}}\setminus\{0\}$ in the Berkovich affine line to the Berkovich projective line…

We study the topology of the punctured disc defined over a non-archimedean field of characteristic zero. Chapter two includes a new proof of the so-called p-adic Riemann existence theorem. This release completes the study of breaks and…

This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean…

We develop non-Archimedean techniques to analyze the degeneration of a sequence of rational maps of the complex projective line. We provide an alternative to Luo's method which was based on ultra-limits of the hyperbolic 3-space. We build…

We prove an Ohsawa-Takegoshi-type extension theorem on the Berkovich closed unit disc over a complete non-Archimedean field. As an application, we establish a non-Archimedean analogue of Demailly's regularization theorem for…

By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As applications, we establish two hyperbolicity-related results.…

Let R be a perfect F_p-algebra, equipped with the trivial norm. Let W(R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate…

Consider a non-archimedean valuation ring V (K its fraction field, in mixed characteristic): inspired by some views presented by Scholze, we introduce a new point of view on the non-archimedean analytic setting in terms of derived analytic…

The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative…

One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative projective surfaces (or, slightly more generally, of noetherian connected graded domains of Gelfand-Kirillov dimension 3). In a…

We define normalized versions of Berkovich spaces over a trivially valued field $k$, obtained as quotients by the action of $\mathbb R_{>0}$ defined by rescaling semivaluations. We associate such a normalized space to any special formal…

We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.

It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate…

Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…

This is an expository article, originally written in Japanese, on a dynamical system over a non-archimedean field. The main viewpoint is from complex and non-archimedean potential theories. After quickly introducing the Berkovich projective…

Generalising a conjecture of Singerman, it is shown that there exist orientably regular chiral hypermaps of every non-spherical type. The proof uses the representation theory of automorphism groups acting on homology and on various spaces…

We present a new proof of Pinchuk's theorem on the analytic continuation of a biholomorphic mapping from a strongly pseudoconvex analytic real hypersurface to a compact strongly pseudoconvex analytic real hypersurface in a complex euclidean…

A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…

A twisted rational map over a non-archimedean field $K$ is the composition of a rational function over $K$ and a continuous automorphism of $K$. We explore the dynamics of some twisted rational maps on the Berkovich projective line.

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite…