On the image of noncommutative local reciprocity map. (English) Zbl 1154.11340

Fesenko, Ivan

Homology Homotopy Appl. 7, No. 3, Conf., 53-62 (2005).

Summary: We recall coherent definitions of two commutative local reciprocity homomorphisms, arithmetic and geometric, and then suggest a new approach to the description of the image of a noncommutative local reciprocity map introduced in [ Adv. Stud. Pure Math. 30, 63–78 (2001; Zbl 1039.11085)] and discuss some of its properties in relation to the commutative maps.

MSC:

11S31	Class field theory; \(p\)-adic formal groups
11S99	Algebraic number theory: local fields

Keywords:

noncommutative reciprocity map; noncommutative local class field theory

Citations:

Zbl 1039.11085