Hilbert's Tenth Problem for function fields over valued fields in characteristic zero

Details Hilbert's Tenth Problem for function fields over valued fields in characteristic zero Hilbert's Tenth Problem for function fields over valued fields in characteristic zero

2009-02-02

arxiv.org/abs/0902.0247v1

Mathematics

Number Theory

Submitted to Algebra & Number Theory

Scientific paper

Let K be a field with a valuation satisfying the following conditions: both K and the residue field k have characteristic zero; the value group is not 2-divisible; there exists a maximal subfield F in the valuation ring such that Gal(\bar{F}/F) and Gal(\bar{k}/k) have the same 2-cohomological dimension and this dimension is finite. Then Hilbert's Tenth Problem has a negative answer for any function field of a variety over K. In particular, this result proves undecidability for varieties over C((T)).

Affiliated with

Also associated with

No associations

Rating

Hilbert's Tenth Problem for function fields over valued fields in characteristic zero 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 function fields over valued fields in characteristic zero, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert's Tenth Problem for function fields over valued fields in characteristic zero will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159612