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Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field

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Compositio Mathematica

Abstract

Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C p and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F.

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Authors and Affiliations

  1. Department of Mathematics, East Carolina University, Greenville, NC, 27858, U.S.A.

    Alexandra Shlapentokh

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  1. Alexandra Shlapentokh
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Shlapentokh, A. Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field. Compositio Mathematica 132, 99–120 (2002). https://doi.org/10.1023/A:1016067603451

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