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arXiv · 1902.03384

Abelianisation of Logarithmic $\mathfrak{sl}_2$-Connections

Nikita Nikolaev
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Abstract

We prove a functorial correspondence between a category of logarithmic $\mathfrak{sl}_2$-connections on a curve $X$ with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover $\pi : \Sigma \to X$. The proof is by constructing a pair of inverse functors $\pi^{\text{ab}}, \pi_{\text{ab}}$, and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor $\pi_\ast$.

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Nikita Nikolaev. 2019-02-09. Abelianisation of Logarithmic $\mathfrak{sl}_2$-Connections. https://doi.org/10.1007/s00029-021-00688-5

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