Endomorphisms of elliptic curves and undecidability in function fields of positive characteristic
نویسندگان
چکیده
منابع مشابه
Undecidability in Function Fields of Positive Characteristic
We prove that the first-order theory of any function field K of characteristic p > 2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.
متن کاملUndecidability in Function Fields of Positive Characteristic
We prove that the first-order theory of any function field K of characteristic p > 2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.
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We prove that the first-order theory of any function field K of characteristic p > 2 is undecidable. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2.
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Let K be a one-variable function field over a field of constants of characteristic 0. Let R be a holomorphy subring of K, not equal to K. We prove the following undecidability results for R: If K is recursive, then Hilbert’s Tenth Problem is undecidable in R. In general, there exist x1, . . . , xn ∈ R such that there is no algorithm to tell whether a polynomial equation with coefficients in Q(x...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.07.016