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Diophantine Undecidability for Some Function Fields of Infinite Transcendence Degree and Positive Characteristic

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Abstract

Let M be a field of positive characteristic p > 0 such that C, the closure of a finite field in M, has an extension of degree p. Let L be a field finitely generated over C and such that M and L are linearly disjoint over C. Then Hilbert’s tenth problem is not decidable over ML. Bibliography: 41 titles.

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  1. Department of Mathematics, East Carolina University, Greenville, NC, 27858, USA

    A. Shlapentokh

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 304, 2003, pp. 141–167.

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Shlapentokh, A. Diophantine Undecidability for Some Function Fields of Infinite Transcendence Degree and Positive Characteristic. J Math Sci 130, 4631–4642 (2005). https://doi.org/10.1007/s10958-005-0358-x

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  • DOI: https://doi.org/10.1007/s10958-005-0358-x

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