Frobenius height of prismatic cohomology with coefficients
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918139473690624 |
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| author | Guo, Haoyang Li, Shizhang |
| author_facet | Guo, Haoyang Li, Shizhang |
| contents | We study the behavior of Frobenius operators on smooth proper pushforwards of prismatic F-crystals. In particular we show that the i-th pushforward has its Frobenius height increased by at most i. Our proof crucially uses the notion of prismatic F-gauges introduced by Drinfeld and Bhatt--Lurie and its relative version, and we give a self-contained treatment without using the stacky formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Frobenius height of prismatic cohomology with coefficients Guo, Haoyang Li, Shizhang Algebraic Geometry Number Theory 14F30, 14G45, 14L05 We study the behavior of Frobenius operators on smooth proper pushforwards of prismatic F-crystals. In particular we show that the i-th pushforward has its Frobenius height increased by at most i. Our proof crucially uses the notion of prismatic F-gauges introduced by Drinfeld and Bhatt--Lurie and its relative version, and we give a self-contained treatment without using the stacky formulation. |
| title | Frobenius height of prismatic cohomology with coefficients |
| topic | Algebraic Geometry Number Theory 14F30, 14G45, 14L05 |
| url | https://arxiv.org/abs/2309.06663 |