Hilbert's Tenth Problem and diophantine sets

01 October 2007 → 30 September 2013
Regional and community funding: Special Research Fund, Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Algebra
    • History and foundations
(un)decidability recursively enumerable diophantine sets
Project description

Hilbert's Tenth Problem is about (un)decibability of diophantine equations. One of the field we study are function fields over valued fields in characteristic 0. Under certain conditions on the valuation and the Galois cohomology we can prove undecidability. We also investigate whether diophantine sets are recursively enumerable for certain polynomial rings, for example over a number field.