Diophantine undecidability of \({\mathbb{C}{}}(t_ 1,t_ 2)\)
The main result of this paper is that the Diophantine theory of the complex function field \(\mathbb{C}(t_ 1,t_ 2)\), where \(t_ 1\) are algebraically independent over the complex numbers, in the language \(\{+,\times,t_ 1,t_ 2,0,1\}\) is undecidable. A model of \((\mathbb{Z},+,\times)\) represented by isogenies of an elliptic curve is also constructed.
scientific article; zbMATH DE number 63892
scientific article