Resumen de Abelianisation of logarithmic \mathfrak {sl}_2-connections

Nikita Nikolaev

• We prove a functorial correspondence between a category of logarithmic sl2-connections on a curve X with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover . The proof is by constructing a pair of inverse functors πab,πab, and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor π∗.