Local Fourier transforms and rigidity for D-modules

Abstract

Local Fourier trnasforms, analogous to the $\ell$-adic Fourier transforms, are constructed for connections over $k((t))$. Following a program of Katz, a meromorphic connection on a curve is shown to be rigid, i.e. determined by local data at the singularities, if and only if a certain cohomological condition is satisfied. We show that the index of rigidity is invariant under Fourier transform.

23 pages

Cited by in corpus (7)

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• Deformations of overconvergent isocrystals on the projective line
• Remarks on rigid irreducible meromorphic connections on the projective line