A study of perfectoid rings via Galois cohomology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917313162248192 |
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| author | Kinouchi, Ryo Shimomoto, Kazuma |
| author_facet | Kinouchi, Ryo Shimomoto, Kazuma |
| contents | In his foundational study of $p$-adic Hodge theory, Faltings introduced the method of almost étale extensions to establish fundamental comparison results of various $p$-adic cohomology theories. Scholze introduced the tilting operations to study algebraic objects arising from $p$-adic Hodge theory in mixed characteristic via the Frobenius map. In this article, we prove a few results which clarify certain ring-theoretic or homological properties of the tilt of an extension between perfectoid rings treated in the construction of big Cohen-Macaulay algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study of perfectoid rings via Galois cohomology Kinouchi, Ryo Shimomoto, Kazuma Commutative Algebra Number Theory In his foundational study of $p$-adic Hodge theory, Faltings introduced the method of almost étale extensions to establish fundamental comparison results of various $p$-adic cohomology theories. Scholze introduced the tilting operations to study algebraic objects arising from $p$-adic Hodge theory in mixed characteristic via the Frobenius map. In this article, we prove a few results which clarify certain ring-theoretic or homological properties of the tilt of an extension between perfectoid rings treated in the construction of big Cohen-Macaulay algebras. |
| title | A study of perfectoid rings via Galois cohomology |
| topic | Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2505.01922 |