Transfers and Unstable Degrees in the $\mathbb{A}^{1}$-Brouwer Degrees Package for Macaulay2
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914160343777280 |
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| author | Atherton, Stephanie Dutta, Somak Garcia, Jordy Lopez Louwsma, Joel Luo, Yuyuan Ong, Wern Juin Gabriel Sagarayaj, Ruzho |
| author_facet | Atherton, Stephanie Dutta, Somak Garcia, Jordy Lopez Louwsma, Joel Luo, Yuyuan Ong, Wern Juin Gabriel Sagarayaj, Ruzho |
| contents | We describe a significant update to the Macaulay2 package A1BrouwerDegrees. We extend several methods in the previous version of the package to the setting of finite étale algebras, allowing the computation of transfers along finite étale extensions. Additionally, we implement a number of new features for the computation of unstable $\mathbb{A}^{1}$-Brouwer degrees and manipulation of classes in the unstable Grothendieck--Witt group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_12765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transfers and Unstable Degrees in the $\mathbb{A}^{1}$-Brouwer Degrees Package for Macaulay2 Atherton, Stephanie Dutta, Somak Garcia, Jordy Lopez Louwsma, Joel Luo, Yuyuan Ong, Wern Juin Gabriel Sagarayaj, Ruzho Algebraic Geometry Algebraic Topology 14F42, 55M25, 68W30, (Primary) 11E04 (Secondary) We describe a significant update to the Macaulay2 package A1BrouwerDegrees. We extend several methods in the previous version of the package to the setting of finite étale algebras, allowing the computation of transfers along finite étale extensions. Additionally, we implement a number of new features for the computation of unstable $\mathbb{A}^{1}$-Brouwer degrees and manipulation of classes in the unstable Grothendieck--Witt group. |
| title | Transfers and Unstable Degrees in the $\mathbb{A}^{1}$-Brouwer Degrees Package for Macaulay2 |
| topic | Algebraic Geometry Algebraic Topology 14F42, 55M25, 68W30, (Primary) 11E04 (Secondary) |
| url | https://arxiv.org/abs/2511.12765 |