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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.21305 |
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| _version_ | 1866908463138865152 |
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| author | Puentes, Andrés Jaramillo Pirisi, Roberto |
| author_facet | Puentes, Andrés Jaramillo Pirisi, Roberto |
| contents | Using Galois-Stiefel-Whitney classes of theta characteristics we show that over a totally real base field the moduli stack of smooth genus $g$ curves and the moduli stack of principally polarized abelian varieties of dimension $g$ have nontrivial cohomological invariants and étale cohomology classes in degree respectively $2^{g-2}, 2^{g-1}$ and $2^{g-1}$. We also compute the pullback from the Brauer group of $\mathcal{M}_3$ to that of $\mathcal{H}_3$ over a general field of characteristic different from $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology classes on moduli of curves from Theta Characteristics Puentes, Andrés Jaramillo Pirisi, Roberto Algebraic Geometry 14F20, 14H10, 14F22 Using Galois-Stiefel-Whitney classes of theta characteristics we show that over a totally real base field the moduli stack of smooth genus $g$ curves and the moduli stack of principally polarized abelian varieties of dimension $g$ have nontrivial cohomological invariants and étale cohomology classes in degree respectively $2^{g-2}, 2^{g-1}$ and $2^{g-1}$. We also compute the pullback from the Brauer group of $\mathcal{M}_3$ to that of $\mathcal{H}_3$ over a general field of characteristic different from $2$. |
| title | Cohomology classes on moduli of curves from Theta Characteristics |
| topic | Algebraic Geometry 14F20, 14H10, 14F22 |
| url | https://arxiv.org/abs/2502.21305 |