Isotropy and full splitting pattern of quasilinear $p$-forms

Kristýna Zemková

doi:10.1016/j.jalgebra.2024.05.017

paper

Isotropy and full splitting pattern of quasilinear $p$ -forms

arXiv:2309.13341 · doi:10.1016/j.jalgebra.2024.05.017

Abstract

For a quasilinear $p$ -form defined over a field $F$ of characteristic $p > 0$ , we prove that its defect over the field $F (p^{n_{1}} a_{1}, \dots, p^{n_{r}} a_{r})$ equals to its defect over the field $F (p a_{1}, \dots, p a_{r})$ , strengthening a result of Hoffmann from 2004. We also compute the full splitting pattern of some families of quasilinear $p$ -forms.

17 pages

Isotropy and full splitting pattern of quasilinear p-forms

Abstract

Isotropy and full splitting pattern of quasilinear $p$ -forms