The Theory of the Entire Algebraic Functions

2023/05/20 by Taylor Dupuy, Ehud Hrushovski, Dupuy, Taylor +1
Computer Science · Mathematics · #03C40 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2305.12226

openalex publication_date 2023/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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