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Hilbert's Tenth Problem for algebraic function fields of characteristic 2

Kirsten Eisentraeger
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Abstract

Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u transcendental over C_K and x algebraic over C(u) and such that K=C_K(u,x). Then Hilbert's Tenth Problem over K is undecidable. Together with Shlapentokh's result for odd characteristic this implies that Hilbert's Tenth Problem for any such field K of finite characteristic is undecidable. In particular, Hilbert's Tenth Problem for any algebraic function field with finite constant field is undecidable.

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BibTeXRIS

Kirsten Eisentraeger. 2002-11-04. Hilbert's Tenth Problem for algebraic function fields of characteristic 2. https://arxiv.org/abs/math/0207029

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