Asian Journal of Mathematics
Volume 8 (2004)
Local Fourier Transforms and Rigidity for D-Modules
Pages: 587 – 606
Local Fourier transforms, analogous to the l-adic local Fourier transforms , are constructed for connections over k((t)). Following a program of Katz , 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 ,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.