Which curves over š¯‘¨ have points with coordinates in a discrete ordered ring?
Lou van den Dries Ā· Transactions of the American Mathematical Society Ā· 1981
A criterion is given for curves defined over Z {\mathbf {Z}} to have an infinite point in a discrete ordered ring. Using this, one can decide effectively whether a given polynomial in Z [ X , Y ] {\mathbf {Z}}[X,Y] has a zero in a model for the axioms of open induction. Riemann-Roch for curves over Q {\mathbf {Q}} is the main tool used.