Neukirch's Approach to the Reciprocity Map and Global Class Field theory in Positive Characteristic

Abstract

Neukirch developed an axiomatic and explicit approach to class field theory. This was applied to local fields and number fields but was never done for global function fields since he believed that geometric approach is more suitable. Nonetheless all the axioms can be verified and we plan to prove that global function fields satisfy the axioms Neukirch developed.