The Ramification Group Filtrations of Elementary Abelian Extensions

Let K be a discrete valuation field with a discrete valuation and associated place P. We investigate the ramification group filtration of an elementary abelian extension LK$ at P. Due to the intimate interplay between the ramification group filtration and the different exponents in all of the sub-extensions of prime degree over K, we can treat number fields, function fields, and local fields simultaneously. The Hasse-Arf property is shown to be true and best possible.

The talk is intended for general audience of basic familiarity with algebraic number theory.