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

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.

arXiv comment17 pages. Comments welcome!