Séminaires à venir

Local class field theory studies and classifies abelian extensions of local fields, which describes the Galois group of the maximal abelian extension of a local field via Artin's local reiprocity map. Let be a finite extension of the -adic number field with its ring of integers . In 1964, Lubin and Tate constructed a 1-dimensional formal group, popularly known as the Lubin-Tate formal group, over and used it to generate a totally ramified maximal abelian extension of the ground field. Moreover, Lubin and Tate offered a new proof of the main theorem (local Artin reciprocity theorem) of local class field theory and thus provided a parallel interpretation of local class field theory. Despite the remarkable applications of the 1-dimensional Lubin-Tate formal group, there has been no suitable generalization of the 1-dimensional to the upper dimension. In this talk, I would like to discuss how one can construct a class of -dimensional formal groups over the ring of -adic integers that provide an actual higher-dimensional analogue of the usual -dimensional Lubin-Tate formal groups. Then, we will see that the -torsion points of such a formal group generate an abelian extension over a certain unramified extension of , and some ramification properties of these abelian extensions.