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

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.

arXiv comment17 pages

References in corpus (2)

• Hoffmann's conjecture for totally singular forms of prime degree
• Isotropy of quadratic forms over function fields in characteristic 2

Cited by in corpus (1)

• Vishik equivalence and similarity of quasilinear $p$-forms and totally singular quadratic forms