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

arXiv Mathematics eprints
 Pub Date:
 July 2002
 arXiv:
 arXiv:math/0207029
 Bibcode:
 2002math......7029E
 Keywords:

 Mathematics  Number Theory;
 11U05 (Primary);
 03B25 (Secondary)
 EPrint:
 19 pages, added two references to original version