Determinants, Delooping and Reciprocity II
Kapranov introduced determinantal theories for Tate spaces in his investigations of 1-dimensional Abelian Langlands correspondences and higher class field theory. Given an idempotent complete exact category, we construct a universal determinantal theory and show that it realizes the K-theory of Tate spaces as a delooping of the K-theory of the exact category. Time permitting, we connect this to the Tame symbol of higher class field theory and we sketch a new proof of Kato reciprocity using the determinant. This is joint work in progress with Braunling, Wolfson, Groechenig.