Year: 2026
Type: preprint
Abstract: Let $F$ be the fraction field of a discrete valuation ring. We give an explicit matrix in $\mathrm{SL}_2(F[X^{\pm1},Y^{\pm1}])\setminus \mathrm{E}_2(F[X^{\pm1},Y^{\pm1}])$. The proof of non-elementarity is based on techniques developed by Peter Abramenko in his preprint arXiv:0808.1095v1.
Source: arXiv (Cornell University)
Authors: Ionin, Vasiliy, Semidetnov, Artem
Institution: University of Geneva
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211908665