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Preprint Number 1502
1502. Philip Dittmann Defining Subrings in Finitely Generated Fields of Characteristic
Not Two E-mail: Submission date: 22 October 2018 Abstract: We give a construction of a family of definable subrings of finitely generated fields K of characteristic not two. We deduce that for any such K there exists a first-order sentence φ_K characterising K in the class of finitely generated fields, i.e. such that for any finitely generated field L we have L ⊧ φ_K if and only if L ≡ K. This answers a question considered by Pop and others, at least when the characteristic is not two. Our method is similar to previous approaches to the question, using Pfister forms and a local-global principle in cohomology. Mathematics Subject Classification: 12L99, 14G25 Keywords and phrases: |

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