Corpus ID: 119142738

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

  title={Abelianisation of Logarithmic \$\mathfrak\{sl\}_2\$-Connections},
  author={Nikita S. Nikolaev},
  journal={arXiv: Algebraic Geometry},
  • Nikita S. Nikolaev
  • Published 2019
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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 $\pi_\ast$.