Investigations into Local Class Field Theory with General Residue Fields - Hall, Christopher Stephen (2023)
Local Fields, complete discrete valuation fields with a finite residue field, are an important mathematical tool in number theory; in particular in the topics of Class Field Theory and Arithmetic Geometry. However, while a lot of work has been done on when the residue field, $\overline{F}$, of the complete discrete valuation field, $F$, is finite; dealing with less restrictions on the fields is also an incredibly fruitful undertaking. This enterprise, both examining some of the work already done on this topic and also expanding on them, is the focus of the thesis.