The Diophantine problem in isotropic reductive groups

Egor Voronetsky

The Diophantine problem in isotropic reductive groups

Number Theory 2025-12-15 v2 Group Theory Logic

Authors: Egor Voronetsky

Abstract

We begin to study model-theoretic properties of non-split isotropic reductive group schemes. In this paper we show that the base ring $K$ is e-interpretable in the point group $G(K)$ of every sufficiently isotropic reductive group scheme $G$ . In particular, the Diophantine problems in $K$ and $G(K)$ are equivalent. We also compute the centralizer of the elementary subgroup of $G(K)$ and the common normalizer of all its root subgroups.

Keywords

algebraic k-theory field theory

Cite

@article{arxiv.2504.14364,
  title  = {The Diophantine problem in isotropic reductive groups},
  author = {Egor Voronetsky},
  journal= {arXiv preprint arXiv:2504.14364},
  year   = {2025}
}

Comments

Extended bibliography, simplified proof of theorem 5, and fixed definition of isotropic reductive group schemes

The Diophantine problem in isotropic reductive groups

Abstract

Keywords

Cite

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