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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00647 |
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| _version_ | 1866910627056844800 |
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| author | Kim, Hyungseop |
| author_facet | Kim, Hyungseop |
| contents | We study a construction of diagrams of dualizable presentable stable $\infty$-categories associated with certain fiber-cofiber sequences over rigid bases, which are sent by localizing invariants, in particular continuous K-theory, to limit diagrams. We apply this to investigate two closely related types of diagrams pertinent to the formal gluing situation; we recover Clausen--Scholze's gluing of continuous K-theory along punctured tubular neighborhoods via Efimov's nuclear module category, and we verify a continuous version of adelic descent statement for localizing invariants on dualizable categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some formal gluing diagrams for continuous K-theory Kim, Hyungseop K-Theory and Homology Algebraic Geometry We study a construction of diagrams of dualizable presentable stable $\infty$-categories associated with certain fiber-cofiber sequences over rigid bases, which are sent by localizing invariants, in particular continuous K-theory, to limit diagrams. We apply this to investigate two closely related types of diagrams pertinent to the formal gluing situation; we recover Clausen--Scholze's gluing of continuous K-theory along punctured tubular neighborhoods via Efimov's nuclear module category, and we verify a continuous version of adelic descent statement for localizing invariants on dualizable categories. |
| title | Some formal gluing diagrams for continuous K-theory |
| topic | K-Theory and Homology Algebraic Geometry |
| url | https://arxiv.org/abs/2410.00647 |