Connections on the total Picard sheaf and the KP hierarchy

A family of connections is introduced on a direct limit of Poincaré sheaves of a curve. These connections descend to connections on the corresponding direct limit of Picard sheaves, defined globally on the Jacobian of the curve. All such connections are classified; in particular they are all flat. Krichever's algebro-geometric solutions of the KP equations are recovered upon trivializing the resulting \tdD-modules over the complement of the divisor.Supported in part by NSF grant no. 58-1353149.