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arXiv · 2603.23978

On Selmer complexes, Stark systems and derived $p$-adic heights

Daniel Macias Castillo·Takamichi Sano
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Abstract

We develop the theory of Nekov\'a\v{r}'s Selmer complexes. We prove that, under mild hypotheses, Nekov\'a\v{r}'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 Nekov\'a\v{r}.

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Daniel Macias Castillo, Takamichi Sano. 2026-03-25. On Selmer complexes, Stark systems and derived $p$-adic heights. https://arxiv.org/abs/2603.23978

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