Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings
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| Format: | Preprint |
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2022
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| _version_ | 1866911223903158272 |
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| author | Ishiro, Shinnosuke Nakazato, Kei Shimomoto, Kazuma |
| author_facet | Ishiro, Shinnosuke Nakazato, Kei Shimomoto, Kazuma |
| contents | To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants and finiteness properties. Using this, we also provide a comparison result on étale cohomology groups under the tilting. As an application, we prove finiteness of the prime-to-$p$-torsion subgroup of the divisor class group of a local log-regular ring that appears in logarithmic geometry in the mixed characteristic case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_16400 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings Ishiro, Shinnosuke Nakazato, Kei Shimomoto, Kazuma Commutative Algebra Algebraic Geometry Number Theory To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants and finiteness properties. Using this, we also provide a comparison result on étale cohomology groups under the tilting. As an application, we prove finiteness of the prime-to-$p$-torsion subgroup of the divisor class group of a local log-regular ring that appears in logarithmic geometry in the mixed characteristic case. |
| title | Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2203.16400 |