On Selmer complexes, Stark systems and derived $p$-adic heights
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910070818734080 |
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| author | Castillo, Daniel Macias Sano, Takamichi |
| author_facet | Castillo, Daniel Macias Sano, Takamichi |
| contents | We develop the theory of Nekovář's Selmer complexes. We prove that, under mild hypotheses, Nekovář's Selmer complexes are canonically quasi-isomorphic to ``Poitou-Tate complexes", which arise from Poitou-Tate global duality exact sequences. We give two applications. Firstly, we prove that the determinant of a Selmer complex is canonically isomorphic to the module of Stark systems and, by using this result, we construct a canonical ``Heegner point Stark system" which controls Selmer groups. Secondly, we prove that the derived $p$-adic height pairing of Bertolini-Darmon concides with that of Nekovář. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Selmer complexes, Stark systems and derived $p$-adic heights Castillo, Daniel Macias Sano, Takamichi Number Theory We develop the theory of Nekovář's Selmer complexes. We prove that, under mild hypotheses, Nekovář's Selmer complexes are canonically quasi-isomorphic to ``Poitou-Tate complexes", which arise from Poitou-Tate global duality exact sequences. We give two applications. Firstly, we prove that the determinant of a Selmer complex is canonically isomorphic to the module of Stark systems and, by using this result, we construct a canonical ``Heegner point Stark system" which controls Selmer groups. Secondly, we prove that the derived $p$-adic height pairing of Bertolini-Darmon concides with that of Nekovář. |
| title | On Selmer complexes, Stark systems and derived $p$-adic heights |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.23978 |