Pullback along the Abel-Jacobi map over the twistor-P1 induces an equivalence on Picard groupoids, recovering archimedean local class field theory via Scholze's geometrisation framework.
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Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).
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Modular variants of p-adic fundamental sequence
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).