The Theory of the Entire Algebraic Functions
Logic
2023-12-12 v2 Number Theory
Abstract
Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a decidable theory (see Prestel-Schmid and van den Dries-A. Macintyre).
Cite
@article{arxiv.2305.12226,
title = {The Theory of the Entire Algebraic Functions},
author = {Taylor Dupuy and Ehud Hrushovski},
journal= {arXiv preprint arXiv:2305.12226},
year = {2023}
}