Mathematics Colloquium



Department of Mathematics
University of Nebraska at Omaha


WHEN:
Thursday, November 13, 2008 at 2:30 PM

WHERE:
Durham Science Center 115

WHAT:


Paul Truman

University of Exeter


will give a talk on

Hopf Algebras in Galois module Theory


ABSTRACT:
Given a finite Galois extension of local fields or number fields L/K with Galois group G, classical Galois module theory seeks to describe the ring of algebraic integers OL as a module over the integral group ring OK[G]. In Hopf-Galois module theory, the Galois group is replaced with a (possibly non-unique) Hopf algebra, and the structure of OL relative to this Hopf algebra is studied. In the case that more than one Hopf algebra can be attached to the extension, we can compare the behaviour of OL relative to each Hopf algebra. This talk shall give an overview of this theory, and include some applications to both wildly and tamely ramified extensions.


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