Local Fourier transforms and rigidity for D-modules

الأصل · EN

Local Fourier trnasforms, analogous to the ℓ-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.