Almost mathematics, Persistence module, and Tamarkin category
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915263540101120 |
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| author | Kuwagaki, Tatsuki Zhang, Bingyu |
| author_facet | Kuwagaki, Tatsuki Zhang, Bingyu |
| contents | We precisely uniform 3 theories that are widely used for symplectic geometers: (Almost) modules over Novikov ring, Persistence module, and Tamarkin category. Along with our method, we also give a neat understanding and language for the related results, in particular, Vaintrob's Novikov/log-perfectoid mirror symmetry for Novikov toric varieties. The results of this paper can also be treated as a study of persistent homology from a higher algebra point of view. Some of our results are shown in the literature, but our method is higher-categorical and sophisticated.
As applications, we discuss a Novikov ring coefficient homological mirror symmetry for toric varieties and propose a conjecture for Novikov ring coefficient homological mirror symmetry for log Calabi-Yau varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost mathematics, Persistence module, and Tamarkin category Kuwagaki, Tatsuki Zhang, Bingyu Symplectic Geometry Algebraic Geometry Algebraic Topology Category Theory We precisely uniform 3 theories that are widely used for symplectic geometers: (Almost) modules over Novikov ring, Persistence module, and Tamarkin category. Along with our method, we also give a neat understanding and language for the related results, in particular, Vaintrob's Novikov/log-perfectoid mirror symmetry for Novikov toric varieties. The results of this paper can also be treated as a study of persistent homology from a higher algebra point of view. Some of our results are shown in the literature, but our method is higher-categorical and sophisticated. As applications, we discuss a Novikov ring coefficient homological mirror symmetry for toric varieties and propose a conjecture for Novikov ring coefficient homological mirror symmetry for log Calabi-Yau varieties. |
| title | Almost mathematics, Persistence module, and Tamarkin category |
| topic | Symplectic Geometry Algebraic Geometry Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2503.15933 |