On the higher analytic vectors of $\mathbf{B}_e$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915093291204608 |
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| author | Steingart, Rustam |
| author_facet | Steingart, Rustam |
| contents | We prove that the first derived analytic vectors of the subring of Fontaine's period ring $\mathbf{B}_e$ stable under the kernel of the cyclotomic character are non-zero. Subsequently we compute their analytic cohomology. We also give a description of the cokernel of the restriction of a variant of the Bloch-Kato exponential map for $\mathbb{Q}_p(n)$ to analytic vectors in terms of derived analytic vectors. In order to achieve the above, we relate pro-analytic vectors with derived analytic vectors in condensed mathematics for regular LF-spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the higher analytic vectors of $\mathbf{B}_e$ Steingart, Rustam Number Theory We prove that the first derived analytic vectors of the subring of Fontaine's period ring $\mathbf{B}_e$ stable under the kernel of the cyclotomic character are non-zero. Subsequently we compute their analytic cohomology. We also give a description of the cokernel of the restriction of a variant of the Bloch-Kato exponential map for $\mathbb{Q}_p(n)$ to analytic vectors in terms of derived analytic vectors. In order to achieve the above, we relate pro-analytic vectors with derived analytic vectors in condensed mathematics for regular LF-spaces. |
| title | On the higher analytic vectors of $\mathbf{B}_e$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.18805 |