Kernels in the Category of Formal Group Laws

Fontaine described the category of formal groups over the ring of Witt vectors over a finite field of characteristic $p$ with the aid of triples consisting of the module of logarithms, the Dieudonné module, and the morphism from the former to the latter. We propose an explicit construction for the kernels in this category in term of Fontaine's triples. The construction is applied to the formal norm homomorphism in the case of an unramified extension of ${{\mathbb{Q}}_{p}}$ and of a totally ramified extension of degree less or equal than $p$ . A similar consideration applied to a global extension allows us to establish the existence of a strict isomorphism between the formal norm torus and a formal group law coming from $L$ -series.