On the middle convolution

2003/05/22 by Michael Dettweiler, Dettweiler, Michael, Stefan Reiter +1 · 1 citation
Mathematics · #34A05 #34M35 #34M50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CA #msc:34A05 #msc:34M35 #msc:34M50

paper · pdf · doi:10.48550/arxiv.math/0305311

arxiv created 2003/05/22 · openalex publication_date 2003/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a cohomological interpretation of the middle convolution functor MC and find an explicit Riemann-Hilbert correspondence for MC_λ. This leads to an algorithm for the construction of Fuchsian systems which correspond to irreducible rigid local systems under the Riemann-Hilbert correspondence. Also, the effect of MC_λon the p-curvatures ist determined and new examples of differential systems are found which satisfy the Grothendieck-Katz p-curvature conjecture.

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• Painlevé equations and the middle convolution

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