P-adic periods of one-dimensional commutative formal groups

A n-dimension commutative formal group over a commutative ring R can be described in a general context, with very restrictive results. However if we restrict ourselves to the one-dimensional case over a p-adic integer ring, we get much more precised and accurate results, from their construction to their classification. The classification gives us a very important invariant of the class, which is the height. In addition to that there is a second invariant for a class, that is the Tate module attached to it. The latter invariant is a key tool for constructing algebraic and arithmetic structures attached to a formal group (the class). In this project we will discuss the p-adic period which at some extend is an invariant for the class of a commutative one-dimensional formal group over a p-adic ring.