Hilbert's tenth problem for rings of algebraic functions in one variable over fields of constants of positive characteristic

Author:
Alexandra Shlapentokh

Journal:
Trans. Amer. Math. Soc. **333** (1992), 275-298

MSC:
Primary 11U05; Secondary 14H05

DOI:
https://doi.org/10.1090/S0002-9947-1992-1091233-2

MathSciNet review:
1091233

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Abstract: The author builds an undecidable model of integers with certain relations and operations in the rings of -integers of algebraic function fields in one variable over fields of constants of positive characteristic, in order to show that Hilbert's Tenth Problem has no solution there.

**[1]**Martin Davis, Yuri Matijasevič, and Julia Robinson,*Hilbert’s tenth problem: Diophantine equations: positive aspects of a negative solution*, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Vol. XXVIII, Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R. I., 1976, pp. 323–378. (loose erratum). MR**0432534****[2]**J. Denef,*The Diophantine problem for polynomial rings of positive characteristic*, Logic Colloquium ’78 (Mons, 1978) Stud. Logic Foundations Math., vol. 97, North-Holland, Amsterdam-New York, 1979, pp. 131–145. MR**567668****[3]**Claude Chevalley,*Introduction to the Theory of Algebraic Functions of One Variable*, Mathematical Surveys, No. VI, American Mathematical Society, New York, N. Y., 1951. MR**0042164**

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1091233-2

Article copyright:
© Copyright 1992
American Mathematical Society