The boundary map in K-theory localization at K_2 is the tame symbol. It sees the tamely ramified part of the Hilbert symbol, but no wild ramification. Gillet has shown how to prove Weil reciprocity using such boundary maps. This implies Hilbert reciprocity for curves over finite fields. However, phrasing Hilbert reciprocity for number fields in a similar way fails because it crucially hinges on wild ramification effects. I will explain how one can solve this problem (except at p=2) by introducing artificial singularities which "fatten up" K-theory.
Freitag, den 22. April 2022 um 13:30 Uhr, in INF 205, SR A Freitag, den 22. April 2022 at 13:30, in INF 205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. Christian Dahlhausen