Abelianisation of logarithmic \mathfrak {sl}_2-connections

• Nikita Nikolaev ^[1]
  1. [1] University of Sheffield

     University of Sheffield

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 5, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00688-5
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• Resumen

  • 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∗.