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

Kristýna Zemková

doi:10.1016/j.jalgebra.2024.05.017

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arXiv · 2309.13341

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

Kristýna Zemková

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Abstract

For a quasilinear $p$-form defined over a field $F$ of characteristic $p>0$, we prove that its defect over the field $F(\sqrt[p^{n_1}]{a_1}, \dots, \sqrt[p^{n_r}]{a_r})$ equals to its defect over the field $F(\sqrt[p]{a_1}, \dots, \sqrt[p]{a_r})$, strengthening a result of Hoffmann from 2004. We also compute the full splitting pattern of some families of quasilinear $p$-forms.

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Kristýna Zemková. 2023-09-23. Isotropy and full splitting pattern of quasilinear $p$-forms. https://doi.org/10.1016/j.jalgebra.2024.05.017

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