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Rigid irregular connections on ℙ1

Published online by Cambridge University Press:  22 April 2010

D. Arinkin*
Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA (email:
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Katz’s middle convolution algorithm provides a description of rigid connections on ℙ1 with regular singularities. We extend the algorithm by adding the Fourier transform to it. The extended algorithm provides a description of rigid connections with arbitrary singularities.

Research Article
Copyright © Foundation Compositio Mathematica 2010


[1]Arinkin, D., Fourier transform and middle convolution for irregular 𝒟-modules, Preprint (2008), arXiv:math/0808.0699.Google Scholar
[2]Beĭlinson, A. and Bernstein, J., A proof of Jantzen conjectures, I. M. Gel’fand seminar, Advances in Soviet Mathematics, vol. 16 (American Mathematical Society, Providence, RI, 1993), 150.Google Scholar
[3]Bloch, S. and Esnault, H., Local Fourier transforms and rigidity for 𝒟-modules, Asian J. Math. 8 (2004), 587605.CrossRefGoogle Scholar
[4]Braverman, A. and Polishchuk, A., Kazhdan–Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz–Verdier trace formula, Preprint (1998), arXiv:math/9810006.Google Scholar
[5]Brylinski, J.-L., Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques, in Géométrie et analyse microlocales, Astérisque 251 (1986), 3–134.Google Scholar
[6]D’Agnolo, A. and Eastwood, M., Radon and Fourier transforms for 𝒟-modules, Adv. Math. 180 (2003), 452485.CrossRefGoogle Scholar
[7]Katz, N., Gauss sums, Kloosterman sums, and monodromy groups, Annals of Mathematics Studies, vol. 116 (Princeton University Press, Princeton, NJ, 1988).CrossRefGoogle Scholar
[8]Katz, N., Rigid local systems, Annals of Mathematics Studies, vol. 139 (Princeton University Press, Princeton, NJ, 1996).CrossRefGoogle Scholar
[9]Kostov, V., The Deligne–Simpson problem for zero index of rigidity, in Perspectives of complex analysis, differential geometry and mathematical physics (St. Konstantin, 2000) (World Scientific, River Edge, NJ, 2001), 135.Google Scholar
[10]Laumon, G., Transformation de Fourier, constantes d’équations fonctionnelles et conjecture de Weil, Publ. Math. Inst. Hautes Études Sci. 65 (1987), 131210.CrossRefGoogle Scholar
[11]Malgrange, B., Équations différentielles à coefficients polynomiaux, Progress in Mathematics, vol. 96 (Birkhäuser, Boston, MA, 1991).Google Scholar
[12]Simpson, C., Katz’s middle convolution algorithm, Pure Appl. Math. Q. 5 (2009), 781852.CrossRefGoogle Scholar