Toward higher chromatic analogs of elliptic cohomology II

Abstract

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 = p f-1) to a curve C̃(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(C̃(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.