|
|||||
|
|
|
|
|
|
|
|
|
Hilbert’s tenth
problem for algebraic function fields of characteristic 2
Kirsten Eisenträger |
|
Vol. 210 (2003), No. 2, 261–281
|
Abstract |
|
Let K be an algebraic function field of characteristic 2 with constant field CK. 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 CK and x algebraic over C(u) and such that K = CK(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. |
Milestones
Received: 1 July 2002
Revised: 11 September 2002
Published: 1 June 2003
|
Authors |
| Kirsten Eisenträger | |
| Department of Mathematics University of California Berkeley, CA 94720 |
|
|
