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.