Geometric Gauss-Dedekind
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866911000847974400 |
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| author | Bitan, Rony A. |
| author_facet | Bitan, Rony A. |
| contents | Gauss and Dedekind have shown a bijection between the set of $\mathrm{SL}_2(\mathbb{Z})$-equivalence classes of primitive positive definite binary quadratic $\mathbb{Z}$-forms of the discriminant of $\mathbb{Q}(\sqrt{Δ<0})$ and the class group of its ring of integers. Using étale cohomology we show an analogue of this correspondence in the positive characteristic. This leads to the description of the set of genera and to another result analogous to Gauss' one by which any form composed with itself belongs to the principal genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_03917 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Geometric Gauss-Dedekind Bitan, Rony A. Algebraic Geometry 11E16, 11E41, 11R65, 11R29, 11R65, 14F20 Gauss and Dedekind have shown a bijection between the set of $\mathrm{SL}_2(\mathbb{Z})$-equivalence classes of primitive positive definite binary quadratic $\mathbb{Z}$-forms of the discriminant of $\mathbb{Q}(\sqrt{Δ<0})$ and the class group of its ring of integers. Using étale cohomology we show an analogue of this correspondence in the positive characteristic. This leads to the description of the set of genera and to another result analogous to Gauss' one by which any form composed with itself belongs to the principal genus. |
| title | Geometric Gauss-Dedekind |
| topic | Algebraic Geometry 11E16, 11E41, 11R65, 11R29, 11R65, 14F20 |
| url | https://arxiv.org/abs/1912.03917 |