Reconstruction theorems for coadmissible D-cap-modules
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911006575296512 |
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| author | Wiersig, Finn |
| author_facet | Wiersig, Finn |
| contents | We prove a Riemann-Hilbert correspondence for Ardakov-Wadsley's coadmissible D-cap-modules and, more generally, for Bode's $\mathcal{C}$-complexes. More precisely, we show that any given $\mathcal{C}$-complex can be reconstructed out of its solutions. As a corollary, we find that slight modifications of the solution and de Rham functors introduced by the author are fully faithful on $\mathcal{C}$-complexes and, in particular, on coadmissible D-cap-modules. One of the many steps of our proof is the explicit computation of the continuous Galois cohomology of a certain decompletion of $B_{dR}^{+}$ which we call the positive overconvergent de Rham period ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction theorems for coadmissible D-cap-modules Wiersig, Finn Algebraic Geometry Number Theory 14G22, 14F10, 14G45, 14C30 We prove a Riemann-Hilbert correspondence for Ardakov-Wadsley's coadmissible D-cap-modules and, more generally, for Bode's $\mathcal{C}$-complexes. More precisely, we show that any given $\mathcal{C}$-complex can be reconstructed out of its solutions. As a corollary, we find that slight modifications of the solution and de Rham functors introduced by the author are fully faithful on $\mathcal{C}$-complexes and, in particular, on coadmissible D-cap-modules. One of the many steps of our proof is the explicit computation of the continuous Galois cohomology of a certain decompletion of $B_{dR}^{+}$ which we call the positive overconvergent de Rham period ring. |
| title | Reconstruction theorems for coadmissible D-cap-modules |
| topic | Algebraic Geometry Number Theory 14G22, 14F10, 14G45, 14C30 |
| url | https://arxiv.org/abs/2506.12601 |