The ramification group filtrations of certain function field extensions
Pacific Journal of Mathematics
We investigate the ramification group filtration of a Galois extension of function fields, if the Galois group satisfies a certain intersection property. For finite groups, this property is implied by having only elementary abelian Sylow p-subgroups. Note that such groups could be nonabelian. We show how the problem can be reduced to the totally wild ramified case on a pextension. Our methodology is based on an intimate relationship between the ramification groups of the field extension and those of all degree- p subextensions. Not only do we confirm that the Hasse-Arf property holds in this setting, but we also prove that the Hasse-Arf divisibility result is the best possible by explicit calculations of the quotients, which are expressed in terms of the different exponents of all those degree- p subextensions.
Castañeda, Jeffrey A. and Wu, Qingquan, "The ramification group filtrations of certain function field extensions" (2015). Mathematics & Physics Faculty Publications. 13.