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arXiv · 2410.18805

On the higher analytic vectors of $\mathbf{B}_e$

Rustam Steingart
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Abstract

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.

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Rustam Steingart. 2024-10-24. On the higher analytic vectors of $\mathbf{B}_e$. https://arxiv.org/abs/2410.18805

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