Gauss-Manin determinants for rank 1 irregular connections on curves

Let f : U --> Spec (K) be a smooth open curve over a field K superset of k, where k is an algebraically closed field of characteristic 0. Let del : L --> L circle times Omega (1)(U/k) be a (possibly irregular) absolutely inte grable connection on a line bundle L. A formula is given for the determinan t of de Rham cohomology with its Gau beta -Manin connection ( det Rf(*) (L circle times Omega (1)(U/K) ), det del (GM) ). The formula is expressed as a norm from the curve of a cocycle with values in a complex defining algebr aic differential characters [7], and this cocycle is shown to exist for con nections of arbitrary rank.