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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01404 |
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| _version_ | 1866917028442406912 |
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| author | Gigli, Pietro |
| author_facet | Gigli, Pietro |
| contents | In this paper, we study the $η$-completed part of the motivic spectrum $\text{MSp}$ constructed by Panin and Walter, representing the universal $\text{Sp}$-oriented cohomology theory. In particular, we investigate the inclusion $(\text{MSp}^\wedge_η)^*\hookrightarrow \text{MGL}^*$ of the cofficient rings, by studying the motivic Adams spectral sequence associated to $\text{MSp}$, mimiking a strategy used by Levine,Yang, Zhao for $\text{MSL}^*$. In order to give a description of $(\text{MSp}^\wedge_η)^*$, we refine the Pontryagin-Thom construction in a way that allows one to obtain symplectic bordism classes from a large family of varieties that carry a certain "symplectic twist", and we prove a criterion to select generators among these classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generators of the algebraic symplectic bordism ring Gigli, Pietro Algebraic Geometry In this paper, we study the $η$-completed part of the motivic spectrum $\text{MSp}$ constructed by Panin and Walter, representing the universal $\text{Sp}$-oriented cohomology theory. In particular, we investigate the inclusion $(\text{MSp}^\wedge_η)^*\hookrightarrow \text{MGL}^*$ of the cofficient rings, by studying the motivic Adams spectral sequence associated to $\text{MSp}$, mimiking a strategy used by Levine,Yang, Zhao for $\text{MSL}^*$. In order to give a description of $(\text{MSp}^\wedge_η)^*$, we refine the Pontryagin-Thom construction in a way that allows one to obtain symplectic bordism classes from a large family of varieties that carry a certain "symplectic twist", and we prove a criterion to select generators among these classes. |
| title | Generators of the algebraic symplectic bordism ring |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.01404 |