$q$-bic forms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913798637486080 |
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| author | Cheng, Raymond |
| author_facet | Cheng, Raymond |
| contents | A $q$-bic form is a pairing $V \times V \to \mathbf{k}$ that is linear in the second variable and $q$-power Frobenius linear in the first; here, $V$ is a vector space over a field $\mathbf{k}$ containing the finite field on $q^2$ elements. This article develops a geometric theory of $q$-bic forms in the spirit of that of bilinear forms. I find two filtrations intrinsically attached to a $q$-bic form, with which I define a series of numerical invariants. These are used to classify, study automorphism group schemes of, and describe specialization relations in the parameter space of $q$-bic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09929 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $q$-bic forms Cheng, Raymond Algebraic Geometry Number Theory 14G17, 11E99, 14D15 (primary), 12H10, 14L35, 14M99 (secondary) A $q$-bic form is a pairing $V \times V \to \mathbf{k}$ that is linear in the second variable and $q$-power Frobenius linear in the first; here, $V$ is a vector space over a field $\mathbf{k}$ containing the finite field on $q^2$ elements. This article develops a geometric theory of $q$-bic forms in the spirit of that of bilinear forms. I find two filtrations intrinsically attached to a $q$-bic form, with which I define a series of numerical invariants. These are used to classify, study automorphism group schemes of, and describe specialization relations in the parameter space of $q$-bic forms. |
| title | $q$-bic forms |
| topic | Algebraic Geometry Number Theory 14G17, 11E99, 14D15 (primary), 12H10, 14L35, 14M99 (secondary) |
| url | https://arxiv.org/abs/2301.09929 |