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

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

Zbl 1039.11085
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