Year: 2025
Type: article
Abstract: Let $R$ be a commutative local ring. We provide an explicit presentation of the symmetric Grothendieck-Witt ring $\mathrm{GW}^{\mathrm{s}}(R)$ of $R$ as an abelian group when $R$ has residue field $\mathbb{F}_2$. This completes a recent work by Rogers and Schlichting, where an explicit presentation of $\mathrm{GW}^{\mathrm{s}}(R)$ is given when the residue field is different from $\mathbb{F}_2$. We then use this result to compute the symmetric Grothendieck-Witt rings for the sequences of local rings $\mathbb{Z}/2^n\mathbb{Z}$ and $\mathbb{F}_2[x]/(x^n)$.
Source: Annals of K-Theory
Author: Marcus Nicolas
Institution: Ludwig-Maximilians-UniversitƤt MĆ¼nchen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416117184