Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields
Copyright policy )Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields
Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n >= 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension >= 1 is undecidable.
19 pages; to appear in Journal of Algebra
- University of Michigan–Ann Arbor United States
- Institute for Advanced Study United States
- University of Michigan–Flint United States
- University of Michigan United States
- Department of Mathematics University of Michigan United States
Decidability (number-theoretic aspects), Diophantine model, Algebra and Number Theory, Arithmetic theory of algebraic function fields, Mathematics - Number Theory, 11U05 (Primary), Undecidability, Basic properties of first-order languages and structures, 03B25 (Secondary), Hilbert's tenth Problem, Hilbert's Tenth Problem, FOS: Mathematics, Elliptic curves, 11U05 (Primary); 03B25 (Secondary), Rational points, Number Theory (math.NT), Quadratic forms
Decidability (number-theoretic aspects), Diophantine model, Algebra and Number Theory, Arithmetic theory of algebraic function fields, Mathematics - Number Theory, 11U05 (Primary), Undecidability, Basic properties of first-order languages and structures, 03B25 (Secondary), Hilbert's tenth Problem, Hilbert's Tenth Problem, FOS: Mathematics, Elliptic curves, 11U05 (Primary); 03B25 (Secondary), Rational points, Number Theory (math.NT), Quadratic forms
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