The Rank of the Cartier operator on Picard Curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911773744955392 |
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| author | Nourozi, Vahid Rahmati, Farhad |
| author_facet | Nourozi, Vahid Rahmati, Farhad |
| contents | For an algebraic curve $\mathcal{X}$ defined over an algebraically closed field of characteristic $p > 0$, the $a$-number $a(\mathcal{X})$ is the dimension of the space of exact holomorphic differentials on $\mathcal{X}$. We compute the $a$-number for a family of certain Picard curves, using the action of the Cartier operator on $H^0(\mathcal{X},Ω^1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Rank of the Cartier operator on Picard Curves Nourozi, Vahid Rahmati, Farhad Algebraic Geometry Number Theory For an algebraic curve $\mathcal{X}$ defined over an algebraically closed field of characteristic $p > 0$, the $a$-number $a(\mathcal{X})$ is the dimension of the space of exact holomorphic differentials on $\mathcal{X}$. We compute the $a$-number for a family of certain Picard curves, using the action of the Cartier operator on $H^0(\mathcal{X},Ω^1)$. |
| title | The Rank of the Cartier operator on Picard Curves |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2306.07823 |