Local Fourier transforms and rigidity for D-modules

Spencer Bloch; Hélène Esnault

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arXiv · math/0312343

Local Fourier transforms and rigidity for D-modules

Spencer Bloch·Hélène Esnault

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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.

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Spencer Bloch, Hélène Esnault. 2003-12-17. Local Fourier transforms and rigidity for D-modules. https://arxiv.org/abs/math/0312343

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