Fumiharu Kato

Tokyo Institute of Technology

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Gunther Cornelissen

Utrecht University

Aristides Kontogeorgis

National and Kapodistrian University of Athens

Daniel Allcock

North Bristol NHS Trust

Janne Kool

Max Planck Institute for Mathematics

Nobuo Tsuzuki

Tohoku University

Nicolas Daire

Laboratoire de Géologie de l’École Normale Supérieure

Yves André

Institut de Mathématiques de Jussieu-Paris Rive Gauche

Yoshiaki Uchino

Tokyo Institute of Technology

Kazuhiro Fujiwara

Nagoya University

Gal Binyamini

Weizmann Institute of Science

Cooperative Institutions

Université Paris Cité

Centre National de la Recherche Scientifique

The University of Tokyo

Tohoku University

Max Planck Institute for Mathematics

Max Planck Society

Nagoya University

Mathematical Institute of the Slovak Academy of Sciences

University of Padua

Utrecht University

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A fake projective plane via 2-adic uniformization with torsion

Tohoku Mathematical Journal (2017)

Daniel Allcock Fumiharu Kato

We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in ${\rm PSL}_3(\mathbb{Q}_2)$ that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake plane yet distinct from it and the other fake planes that arise from 2-adic uniformization by torsion-free groups. As part of the proof, and of independent interest, we compute the homotopy type of the Berkovich space of our plane.

Uniformization (probability theory)

Real projective plane

Lattice (music)

10.2748/tmj/1498269624

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Citations (4)

[Life in the primitive period and nursing (1). Life and health maintenance during the Jomon period (from 8000 B. C. to 200 B. C].

PubMed (1987)

Eiko Endo M Sakamoto Fumiharu Kato M Takahashi Y Kamisaka

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Three examples of the relation between rigid-analytic and algebraic deformation parameters

arXiv (Cornell University) (2008)

Gunther Cornelissen Fumiharu Kato Aristides Kontogeorgis

We consider three examples of families of curves over a non-archimedean valued field which admit a non-trivial group action. These equivariant deformation spaces can be described by algebraic parameters (in the equation of the curve), or by rigid-analytic parameters (in the Schottky group of the curve). We study the relation between these parameters as rigid-analytic self-maps of the disk.

10.48550/arxiv.0809.4579

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On Henselian Rigid Geometry

arXiv (Cornell University) (2017)

Fumiharu Kato

We overview some of the foundations of the so-called henselian rigid geometry, and show that henselian rigid geometry has many aspects, useful in applications, that one cannot expect in the usual rigid geometry. This is done by announcing a few characteristic results, one of which is an analogue of Zariski Main Theorem.

10.48550/arxiv.1702.00679

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LOG SMOOTH DEFORMATION AND MODULI OF LOG SMOOTH CURVES

International Journal of Mathematics (2000)

Fumiharu Kato

The aim of this paper is to define a reasonable moduli theory of log smooth curves which recovers the classical Deligne–Knudsen–Mumford moduli of pointed stable curves.

10.1142/s0129167x0000012x

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Citations (142)

Extremal quasimodular forms of lower depth with integral Fourier coefficients

arXiv (Cornell University) (2021)

Tsudoi Kaminaka Fumiharu Kato

We show that, based on Grabner's recent results on modular differential equations satisfied by quasimodular forms, there exist only finitely many normalized extremal quasimodular forms of depth $r$ that have all Fourier coefficients integral for each of $r=1,2,3,4$, and partly classifies them, where the classification is complete for $r=2,3,4$; in fact, we show that there exists no normalized extremal quasimodular forms of depth $4$ with all Fourier coefficients integral. Our result disproves a conjecture by Pellarin.

10.48550/arxiv.2101.09897

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Integral morphisms and log blow-ups

arXiv (Cornell University) (2021)

Fumiharu Kato

This paper is a revision of the author's old preprint "Exactness, integrality, and log modifications". We will prove that any quasi-compact morphism of fs log schemes can be modified locally on the base to an integral morphism by base change by fs log blow-ups.

Morphism

Preprint

Base (topology)

10.48550/arxiv.2101.09104

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Exactness, integrality, and log modifications

arXiv (Cornell University) (1999)

Fumiharu Kato

In this paper we discuss log blow-up's, introduced by Kazuya Kato, and define the concept of log modifications. Using this concept we prove that any morphism f: X ---> Y of locally noetherian fs log schemes with underlying structures of f and Y quasi-compact can be modified to an exact morphism, and moreover to an integral morphism. By a well-known fact on the underlying structure of an integral morphism this result can be considered as a weak log-version of flattening theorem by Raynaud and Gruson.

Morphism

Flattening

10.48550/arxiv.math/9907124

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Citations (13)

Arithmetic structure of CMSZ fake projective planes

Journal of Algebra (2006)

Fumiharu Kato Hiroyuki Ochiai

Corollary

10.1016/j.jalgebra.2006.07.019

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Mumford curves with maximal automorphism group II: Lame type groups in genus 5-8

arXiv (Cornell University) (2002)

Gunther Cornelissen Fumiharu Kato

A Mumford curve of genus g=5,6,7 or 8 over a non-archimedean field of characteristic p (such that if p=0, the residue field characteristic exceeds 5) has at most 12(g-1) automorphisms. In this paper, all curves that attain this bound and their automorphism groups (called of Lame type) are explicitly determined.

10.48550/arxiv.math/0207246

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