Universally defining subrings in function fields
Abstract
Abstract We establish that all rings of 𝑆-integers are universally definable in function fields in one variable over certain ground fields including global and non-archimedean local fields. That is, we show that the complement of such a ring of 𝑆-integers is always a diophantine set. As a technical tool, we use a reciprocity exact sequence for quadratic Witt groups in function fields over almost arbitrary base fields (of any characteristic), which is new and of potentially independent interest.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Topology and Set Theory
advanced mathematical theories
Publication details
- Journal / source
- Journal fĂĽr die reine und angewandte Mathematik (Crelles Journal)
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 28 April 2026
- Language
- EN