Asian Journal of Mathematics

Volume 8 (2004)

Number 4

Local Fourier Transforms and Rigidity for D-Modules

Pages: 587 – 606

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n4.a16

Authors

Spencer Bloch

Helene Esnault

Abstract

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].

Full Text (PDF format)