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- W2918310474 abstract "Abstract We prove a functorial correspondence between a category of logarithmic $$mathfrak {sl}_2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>sl</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -connections on a curve $${mathsf {X}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>X</mml:mi> </mml:math> with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover Equation missing<!-- image only, no MathML or LaTex -->. The proof is by constructing a pair of inverse functors $$pi ^text {ab}, pi _text {ab}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mtext>ab</mml:mtext> </mml:msup> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>π</mml:mi> <mml:mtext>ab</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor $$pi _*$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>π</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msub> </mml:math> ." @default.
- W2918310474 created "2019-03-11" @default.
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- W2918310474 date "2021-08-03" @default.
- W2918310474 modified "2023-09-27" @default.
- W2918310474 title "Abelianisation of logarithmic $$mathfrak {sl}_2$$-connections" @default.
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