Can "Punctual" Topologies Be Better Than the Etale Topology?

Igor Minevich

April 2, 2013

Stephen Lichtenbaum defined a "Weil-etale" topology for function fields by making a slight modification to the etale topology, but in order to define something similar for number fields, he had to first replace the etale topology with what we call a "punctual" topology, and then use Weil-groups instead of Galois groups. I will explain what all this means and the purpose: its conjectural relationship to special values of zeta functions of number fields. No prerequisites are necessary.