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arXiv · 2305.12226

The Theory of the Entire Algebraic Functions

Taylor Dupuy·Ehud Hrushovski
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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).

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Taylor Dupuy, Ehud Hrushovski. 2023-05-20. The Theory of the Entire Algebraic Functions. https://arxiv.org/abs/2305.12226

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