Let p be a prime and f a positive integer, greater than 1 if p=2. We construct liftings of the Artin-Schreier curve C(p,f) in characteristic p defined by the equation ye=x-xp (where e=pf-1) to a curve C'(p,f) over a certain polynomial ring R' in characteristic 0 which shares the following property with C(p,f). Over a certain quotient of R', the formal completion of the Jacobian J(C'(p,f)) has a 1-dimensional formal summand of height (p-1)f.
Along the way we show how Honda's theory of commutative formal group laws can be extended to more general rings and prove a conjecture of his about the Fermat curve.Homology, Homotopy and Applications, Vol. 10 (2008), No. 3, pp.335-368.