Some ring-theoretic properties of rings via Frobenius and monoidal maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912798392451072 |
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| author | Eto, Kazufumi Horiuchi, Jun Shimomoto, Kazuma |
| author_facet | Eto, Kazufumi Horiuchi, Jun Shimomoto, Kazuma |
| contents | The purpose of this note is to relate certain ring-theoretic properties of rings in mixed and positive characteristics that are related to each other by a tilting operation used in perfectoid geometry. To this aim, we exploit the multiplicative structure of the ``monoidal map", which is constructed on arbitrary $p$-adically complete rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01765 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some ring-theoretic properties of rings via Frobenius and monoidal maps Eto, Kazufumi Horiuchi, Jun Shimomoto, Kazuma Commutative Algebra The purpose of this note is to relate certain ring-theoretic properties of rings in mixed and positive characteristics that are related to each other by a tilting operation used in perfectoid geometry. To this aim, we exploit the multiplicative structure of the ``monoidal map", which is constructed on arbitrary $p$-adically complete rings. |
| title | Some ring-theoretic properties of rings via Frobenius and monoidal maps |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2301.01765 |