D-elliptic sheaves and the Langlands correspondence.
Die geometrische Theorie der algebraischen Funktionen für beliebige vollkommene Körper
Die Struktur der Funktionenkörper zu hyperabelschen Gruppen. II.
Die Ungleichung von Castelnuovo.
Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Differential equations which come from geometry
Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall.
Division algebras that ramify only along a singular plane cubic curve.
Ein Analogon des Satzes von Nagell-Lutz über die Torsion einer elliptischen Kurve.
Einbettungen kommutativer algebraischer Gruppen und einige ihrer Eigenschaften.
Elementary Albeian p-Extensions of Algebraic Function Fields.
Elliptic curves and continued fractions.
Elliptic curves over function fields with a large set of integral points
We construct isotrivial and non-isotrivial elliptic curves over with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily...
Elliptische Funktionenkörper mit schlechter Reduktion.
Erweiterung des Abel'schen Satzes von der Form der algebraisch-logarithmisch ausdrückbaren Integrale algebraischer Functionen
Etale coverings of a Mumford curve
Let the field be complete w.r.t. a non-archimedean valuation. Let be a Mumford curve, i.e. the irreducible components of the stable reduction of have genus 0. The abelian etale coverings of are constructed using the analytic uniformization and the theta-functions on . For a local field one rediscovers . Frey’s description of the maximal abelian unramified extension of the field of rational functions of .
Explicit construction of a global uniformization for an algebraic correspondence.
Factorial Fermat curves over the rational numbers
A polynomial f in the set {Xⁿ+Yⁿ, Xⁿ +Yⁿ-Zⁿ, Xⁿ +Yⁿ+Zⁿ, Xⁿ +Yⁿ-1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.
Field of moduli versus field of definition for cyclic covers of the projective line
We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli that can not be defined over is also given.