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arXiv · 2309.13346

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

Kristýna Zemková
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Abstract

For quadratic forms over fields of characteristic different from two, there is a so-called Vishik criterion, giving a purely algebraic characterization of when two quadratic forms are motivically equivalent. In analogy to that, we define Vishik equivalence on quasiliner $p$-forms. We study the question whether Vishik equivalent $p$-forms must be similiar. We prove that this is not true for quasilinear $p$-forms in general, but we find some families of totally singular quadratic forms (i.e., of quasilinear $2$-forms) for which the question has positive answer.

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Kristýna Zemková. 2023-09-23. Vishik equivalence and similarity of quasilinear $p$-forms and totally singular quadratic forms. https://doi.org/10.2140/pjm.2024.329.327

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