Hilbert's Tenth Problem for algebraic function fields of characteristic 2
Number Theory
2016-09-07 v2
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.
Keywords
Cite
@article{arxiv.math/0207029,
title = {Hilbert's Tenth Problem for algebraic function fields of characteristic 2},
author = {Kirsten Eisentraeger},
journal= {arXiv preprint arXiv:math/0207029},
year = {2016}
}
Comments
19 pages, added two references to original version