Another proof of the almost purity theorem for perfectoid valuation rings
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911474714148864 |
|---|---|
| author | Ishiro, Shinnosuke Shimomoto, Kazuma |
| author_facet | Ishiro, Shinnosuke Shimomoto, Kazuma |
| contents | The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation ring. We give a new proof by exploiting the behavior of Faltings' normalized length under the Frobenius map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_13984 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Another proof of the almost purity theorem for perfectoid valuation rings Ishiro, Shinnosuke Shimomoto, Kazuma Commutative Algebra Algebraic Geometry Number Theory The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation ring. We give a new proof by exploiting the behavior of Faltings' normalized length under the Frobenius map. |
| title | Another proof of the almost purity theorem for perfectoid valuation rings |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2012.13984 |