Irreducibility of polynomials over global fields is diophantine

DOI10.1112/S0010437X17007977zbMath1429.11220arXiv1601.07829WikidataQ130130776 ScholiaQ130130776MaRDI QIDQ4636426

Philip Dittmann

Publication date: 19 April 2018

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.07829

zbMATH Keywords

definabilitycentral simple algebraDiophantine set

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (4)

Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers ⋮ A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY ⋮ Universally defining finitely generated subrings of global fields ⋮ Diophantine definability of nonnorms of cyclic extensions of global fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diophantine classes of holomorphy rings of global fields
• Universally and existentially definable subsets of global fields
• A universal first-order formula defining the ring of integers in a number field
• Explicit theorems on generator polynomials
• Integrality at a prime for global fields and the perfect closure of global fields of characteristic \(p > 2\)
• Le complémentaire des puissances -ièmes dans un corps de nombres est un ensemble diophantien
• Characterizing integers among rational numbers with a universal-existential formula
• Finite-Dimensional Division Algebras over Fields
• Defining \(\mathbb Z\) in \(\mathbb Q\)

This page was built for publication: Irreducibility of polynomials over global fields is diophantine