Formal Group Exponentials and Galois Modules in Lubin-Tate Extensions

The main result of this paper is the construction of overconvergent power series with coefficients in Lubin-Tate extensions of p-adic fields. Using the values of these series at certain units we then construct integral Galois module generators in certain wildly ramified extensions and also obtain a new description of the Galois action in Lubin-Tate extensions of p-adic fields. The motivation for this work came from recent progress with open questions on integral Galois module structure in wildly ramified extensions of number fields as a consequence of explicit descriptions of local integral Galois module generators in certain extensions of p-adic fields due to Pickett. In parallel, Pulita has generalized the theory of Dwork's power series to a set of power series with coefficients in Lubin-Tate extensions of Q(p). In this paper, we generalize both Pulita's power series and Pickett's constructions using a combination of several tools: formal group exponentials, ramified Witt vectors and Lubin-Tate theory.