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

2009/02/02 by Jeroen Demeyer, Demeyer, Jeroen
Mathematics · #12L05 (14H05 12J10 03B25 12G10) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #math.LO #math.NT #msc:03B25 #msc:12J10 #msc:12L05

paper · pdf · doi:10.48550/arxiv.0902.0247

Submitted to Algebra & Number Theory

arxiv created 2009/02/02 · arxiv updated 2009/12/01

Abstract

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(F/F) and Gal(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)).

Related

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• Hilbert's Tenth Problem for function fields of characteristic zero
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