Asian Journal of Mathematics

Local Fourier Transforms and Rigidity for D-Modules

Spencer Bloch and Helene Esnault


Local Fourier transforms, analogous to the l-adic local Fourier transforms [14], are constructed for connections over k((t)). Following a program of Katz [12], a meromorphic connection on a curve is shown to ber igid, i.e. determined by local data at the singularities, if and only if a certain infinitesimal rigidity conditionis satisfied. As in [12],the argument uses local Fourier transforms to prove an invariance result for the rigidity index under global Fourier transform. A key technical tool is the notion of good lattice pairs for a connection[5].

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Asian J. Math., Volume 8, Number 4 (2004), 587-606.

First available in Project Euclid: 13 June 2005

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Bloch, Spencer; Esnault, Helene. Local Fourier Transforms and Rigidity for D -Modules. Asian J. Math. 8 (2004), no. 4, 587--606.

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