Mathematics Colloquium

New research results at UNO

Department of Mathematics
University of Nebraska at Omaha

WHEN:
Wednesday, October 20, 2004 at 2:30 PM

WHERE:
Durham Science Center, Room 255

WHAT:

ABSTRACT:
This talk will begin with an introduction to additive Galois structure in local number fields, a topic which lies on the boundary between Number Theory and Integral Representation Theory. After observing that additive Galois structure is dependent upon Hilbert's ramification filtration, we will specialize to fully ramified p-extensions of local number fields (the totally wild extensions). And then we will specialize further to elementary abelian extensions. Here Hilbert's ramification filtration does not provide us with a rich enough source of invariants (to determine additive Galois structure), and we are forced to look for a richer source. We find that truncated exponentiation (a particular truncation of the binomial series) allows the residue field to act upon the elementary abelian Galois group. The result is an interesting generalization of the group and a new ramification filtration. The new breaks are necessary (and sometimes sufficient) for additive Galois structure. This is joint work with Nigel Byott.

    Back to the Mathematics Colloquium Page