Vishik equivalence and similarity of quasilinear $p$-forms and totally singular quadratic forms
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909280181944320 |
|---|---|
| author | Zemková, Kristýna |
| author_facet | Zemková, Kristýna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vishik equivalence and similarity of quasilinear $p$-forms and totally singular quadratic forms Zemková, Kristýna Number Theory Algebraic Geometry 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. |
| title | Vishik equivalence and similarity of quasilinear $p$-forms and totally singular quadratic forms |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2309.13346 |