On the de Rham–Witt Complex over Perfectoid Rings
| Autor: | Christopher Davis, Irakli Patchkoria |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Exact sequence Ring (mathematics) Root of unity General Mathematics 010102 general mathematics Algebraic extension 01 natural sciences Ring of integers Mathematics::K-Theory and Homology 0103 physical sciences Torsion (algebra) Perfectoid 010307 mathematical physics 0101 mathematics Algebraic number Mathematics |
| Zdroj: | International Mathematics Research Notices. 2022:13897-13983 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnab092 |
| Popis: | Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt–Madsen on the $p$-typical absolute de Rham–Witt complex in mixed characteristic. We have two primary results. The 1st result is an exact sequence that describes the kernel of the restriction map on the de Rham–Witt complex over $A$, where $A$ is the ring of integers in an algebraic extension of $\textbf{Q}_p$ or where $A$ is a $p$-torsion-free perfectoid ring. The 2nd result is a description of the $p$-power torsion (and related objects) in the de Rham–Witt complex over $A$, where $A$ is a $p$-torsion-free perfectoid ring containing a compatible system of $p$-power roots of unity. Both of these results are analogous to the results of Hesselholt and Madsen. Our main contribution is the extension of their results to certain perfectoid rings. We also provide algebraic proofs of these results, whereas the proofs of Hesselholt and Madsen used techniques from topology. |
| Databáze: | OpenAIRE |
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