8 papers
Three examples of the relation between rigid-analytic and algebraic deformation parameters
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 b…
Mumford curves with maximal automorphism group II: Lame type groups in genus 5-8
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) automorphi…
Mumford curves with maximal automorphism group
Gunther Cornelissen, Fumiharu Kato
The maximal number of automorphisms of a Mumford curve over a non-archimedean valued field of positive characteristic is known. In this note, the unique family of curves that attai…
Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic
Gunther Cornelissen, Fumiharu Kato
We compute the dimension of the tangent space to, and the Krull dimension of the pro-representable hull of two deformation functors. The first one is the ``algebraic'' deformation…
Arithmetic structure of CMSZ fake projective planes
Fumiharu Kato, Hiroyuki Ochiai
We prove that the fake projective planes constructed from the diadic discrete group discovered by Cartwright, Mantero, Steger, and Zappa are connected Shimura varieties associated…
Graph Theoretic Construction of Discrete Groups over p-adic Fields
Fumiharu Kato
This paper is originally designed as a part of revision of the author's preprint math.AG/9908174 "P-adic Schwarzian triangle groups of Mumford type". Recently, Yves Andr'e pointed…