Abstract:

Reciprocity theorems relate statements of the form "p is an n-adic residue of q" with reciprocal statements of the form "q is an n-adic residue of p."  There is an algebraic K-theory anologue of the reciprocity law, which can be seen as a generalization of reciprocity in higher dimension.  In this talk I will explain the results by Banaszak and Kahn on this topic and propose a different approach for real number fields at prime 2.