On the middle convolution
Abstract
We present a cohomological interpretation of the middle convolution functor MC and find an explicit Riemann-Hilbert correspondence for MCλ. 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 MCλ on the p-curvatures ist determined and new examples of differential systems are found which satisfy the Grothendieck-Katz p-curvature conjecture.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.