2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69640Local 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 pagesAlgebraic Geometry14F40text