Strongly exact mirror identification conjecture

Let R\mathcal{R} be a simple eigenray diagram, let MRM_{\mathcal{R}} be the associated symplectic manifold, let YR\mathcal{Y}_{\mathcal{R}} be the analytification of the scheme constructed from R\mathcal{R}, and let SHVit0(MR)SH^0_{Vit}(M_{\mathcal{R}}) denote the relevant Viterbo symplectic cohomology algebra. Strongly exact mirror conjecture. If R\mathcal{R} is strongly exact and SHVit0(MR)SH^0_{Vit}(M_{\mathcal{R}}) is smooth, then YR\mathcal{Y}_{\mathcal{R}} and Specan(SHVit0(MR)Λ)Spec^{an}(SH^0_{Vit}(M_{\mathcal{R}})\otimes\Lambda) are canonically isomorphic. This is a proposed non-Archimedean mirror-symmetry identification; the source does not state that it has been proved.

Sources & referencesView supporting material

Primary source

Yoel Groman and Umut Varolgunes, “Locality of relative symplectic cohomology for complete embeddings”, arXiv:2110.08891 (2023).

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