Title

The ramification group filtrations of certain function field extensions

Document Type

Article

Publication Title

Pacific Journal of Mathematics

Abstract

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.

First Page

309

Last Page

320

DOI

10.2140/pjm.2015.276.309

Publication Date

1-1-2015

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