A remark about isogenies of elliptic curves over quadratic fields
Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmer-Gruppen gewisser elliptischer Kurven.
Der Rang der Lösungen von Y2 = x3 ...p3 über Q.
Dualitätssatz für endliche kommutative Gruppenschemata über Kongruenzfunktionenkörpern.
Non standard arithmetic and application to height functions
The Way to the Proof of Fermat’s Last Theorem
On Bilinear Structures on Divisor Class Groups
It is well known that duality theorems are of utmost importance for the arithmetic of local and global fields and that Brauer groups appear in this context unavoidably. The key word here is class field theory. In this paper we want to make evident that these topics play an important role in public key cryptopgraphy, too. Here the key words are Discrete Logarithm systems with bilinear structures. Almost all public key crypto systems used today based on discrete logarithms...
Galois representations of octahedral type and 2-coverings of elliptic curves.
On the number of elliptic curves with CM cover large algebraic fields
Elliptic curves with CM unveil a new phenomenon in the theory of large algebraic fields. Rather than drawing a line between and or and they give an example where the line goes beween and and another one where the line goes between and .
The Strong Lefschetz Principle in Algebraic Geometry.
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