The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912160948420608 |
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| author | Di Lorenzo, Andrea Pirisi, Roberto |
| author_facet | Di Lorenzo, Andrea Pirisi, Roberto |
| contents | We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. We achieve this result by computing the low degree cohomological invariants of these stacks. As a corollary we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves Di Lorenzo, Andrea Pirisi, Roberto Algebraic Geometry 14F22, 14H10 We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. We achieve this result by computing the low degree cohomological invariants of these stacks. As a corollary we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two. |
| title | The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves |
| topic | Algebraic Geometry 14F22, 14H10 |
| url | https://arxiv.org/abs/2402.06620 |