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arXiv · 2606.03902

The Abel--Jacobi map over the twistor-$\mathbb{P}^1$ and real local class field theory

Saverio Caleca·Maximilian Hauck
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Abstract

We study the Abel--Jacobi map over the twistor-$\mathbb{P}^1$ in the context of Scholze's geometrisation of the real local Langlands correspondence. In a similar spirit to a result of Fargues over the Fargues--Fontaine curve, we prove that pullback along the Abel--Jacobi map induces an equivalence on Picard groupoids and use this to recover local class field theory for archimedean local fields.

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Saverio Caleca, Maximilian Hauck. 2026-06-02. The Abel--Jacobi map over the twistor-$\mathbb{P}^1$ and real local class field theory. https://arxiv.org/abs/2606.03902

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