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

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

2002-07-03

arxiv.org/abs/math/0207029v2

Mathematics

Number Theory

19 pages, added two references to original version

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Hilbert's Tenth Problem for algebraic function fields of characteristic 2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hilbert's Tenth Problem for algebraic function fields of characteristic 2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert's Tenth Problem for algebraic function fields of characteristic 2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-526337