Application of formal groups to reciprocity laws

Abstract

Formal groups are easily defined algebraic objects that have a wide range of applications in many field of mathematics from cobordism theory to number theory with the present talk being devoted to the latter. They are defined as formal power series F in two variables such that F(x, 0) = x; F(F(x, y), z) = F(x, F(y, z)) and F(x, y) = F(y, x). A relation between formal groups and reciprocity laws is investigated following the approach by Honda.