The p-adic Corlette–Simpson correspondence for abeloids
- For an abeloid variety A over a complete algebraically closed field extension K of Qp, we construct a p-adic Corlette–Simpson correspondence, namely an equivalence between finite-dimensional continuous K-linear representations of the Tate module and a certain subcategory of the Higgs bundles on A. To do so, our central object of study is the category of vector bundles for the v-topology on the diamond associated to A. We prove that any pro-finite-étale v-vector bundle can be built from pro-finite-étale v-line bundles and unipotent v-bundles. To describe the latter, we extend the theory of universal vector extensions to the v-topology and use this to generalise a result of Brion by relating unipotent v-bundles on abeloids to representations of vector groups.
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| Author: | Ben HeuerORCiD, Lucas MannORCiDGND, Annette WernerORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-695715 |
| DOI: | https://doi.org/10.1007/s00208-022-02371-2 |
| ISSN: | 1432-1807 |
| Parent Title (English): | Mathematische Annalen |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2022/03/07 |
| Date of first Publication: | 2022/03/07 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/09/06 |
| Volume: | 385 |
| Issue: | 3-4 |
| Page Number: | 38 |
| First Page: | 1639 |
| Last Page: | 1676 |
| Note: | Mathematics Subject Classification: 14G45 |
| Note: | Open Access funding enabled and organized by Projekt DEAL. |
| HeBIS-PPN: | 512574561 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] / 14G22 Rigid analytic geometry |
| 14-XX ALGEBRAIC GEOMETRY / 14Kxx Abelian varieties and schemes / 14K15 Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx] | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
