Reconstructing D-cap from p-adic Hodge theory
We construct a solution functor within the context of a still hypothetical p-adic analytic Riemann-Hilbert correspondence. Our approach relies on the overconvergent de Rham period sheaf, obtained from an ind-Banach completion of the infinitesimal period sheaf along the kernel of Fontaine’s map. A ke...
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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2024
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| _version_ | 1824458772512243712 |
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| author | Wiersig, F |
| author2 | Ardakov, K |
| author_facet | Ardakov, K Wiersig, F |
| author_sort | Wiersig, F |
| collection | OXFORD |
| description | We construct a solution functor within the context of a still hypothetical p-adic analytic Riemann-Hilbert correspondence. Our approach relies on the overconvergent de Rham period sheaf, obtained from an ind-Banach completion of the infinitesimal period sheaf along the kernel of Fontaine’s map. A key result in this thesis is establishing a bimodule structure on the overconvergent de Rham period structure sheaf over D-cap and the overconvergent de Rham period sheaf. Here, D-cap denotes the sheaf of infinite order differential operators introduced by Ardakov-Wadsley; notably, the analogous statement does not hold for Scholze’s de Rham period sheaf. We explain how this leads to a solution functor for D-cap modules and propose conjectures about its compatibility with Scholze’s horizontal sections functor and the reconstruction of D-cap-modules from their solutions. |
| first_indexed | 2025-02-19T04:31:12Z |
| format | Thesis |
| id | oxford-uuid:2cef5184-9d48-40e3-9135-eaf9e8ed94d9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:31:12Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | oxford-uuid:2cef5184-9d48-40e3-9135-eaf9e8ed94d92025-01-06T09:58:59ZReconstructing D-cap from p-adic Hodge theoryThesishttp://purl.org/coar/resource_type/c_db06uuid:2cef5184-9d48-40e3-9135-eaf9e8ed94d9MathematicsEnglishHyrax Deposit2024Wiersig, FArdakov, KKremnitzer, YWe construct a solution functor within the context of a still hypothetical p-adic analytic Riemann-Hilbert correspondence. Our approach relies on the overconvergent de Rham period sheaf, obtained from an ind-Banach completion of the infinitesimal period sheaf along the kernel of Fontaine’s map. A key result in this thesis is establishing a bimodule structure on the overconvergent de Rham period structure sheaf over D-cap and the overconvergent de Rham period sheaf. Here, D-cap denotes the sheaf of infinite order differential operators introduced by Ardakov-Wadsley; notably, the analogous statement does not hold for Scholze’s de Rham period sheaf. We explain how this leads to a solution functor for D-cap modules and propose conjectures about its compatibility with Scholze’s horizontal sections functor and the reconstruction of D-cap-modules from their solutions. |
| spellingShingle | Mathematics Wiersig, F Reconstructing D-cap from p-adic Hodge theory |
| title | Reconstructing D-cap from p-adic Hodge theory |
| title_full | Reconstructing D-cap from p-adic Hodge theory |
| title_fullStr | Reconstructing D-cap from p-adic Hodge theory |
| title_full_unstemmed | Reconstructing D-cap from p-adic Hodge theory |
| title_short | Reconstructing D-cap from p-adic Hodge theory |
| title_sort | reconstructing d cap from p adic hodge theory |
| topic | Mathematics |
| work_keys_str_mv | AT wiersigf reconstructingdcapfrompadichodgetheory |