Diophantine Sets of Polynomials over Number Fields

Seminar series

Date

Thu, 28 Jan 2010
17:00

Location

Speaker

Jeroen Demeyer

Organisation

Ghent

Let R be a number field (or a recursive subring of anumber field) and consider the polynomial ring R[T].

We show that the set of polynomials with integercoefficients is diophantine (existentially definable) over R[T].

Applying a result by Denef, this implies that everyrecursively enumerable subset of R[T]^k is diophantine over R[T].