Math 620 Notes - Fall 2009
Faculty: Ted Chinburg
Office Hours: By appointment. I'll organize some Skype office hours in the evening as well.
- Galois Closures of ring extensions:
- An excerpt from a paper by Bhargava
This is from ``Higher composition laws III: The parameterization of quartic rings," by M.
Bhargava, Annals of Math, 159 (2004), p. 1329 -1360. This one of a sequence of four
papers in the Annals by Bhargava which would be interesting to discuss at some
point in the Galois seminar.
- Notes from a Talk by Bhargava given in
Leiden, in April 2009 These notes give some info on recent developments with
Galois closures of rings. One open problems has to do with finding an appropriate generalization
to rings of the field extensions one obtains by adjoining some number (but not all)
of the roots of an irreducible monic equation over the ground field.
- Polynomials which take on integral values on a specified set
- An American Math Monthly article by Bhargava
This is an introduction to the subject.
- A Journal of Number theory article by Bhargava
This article gives more details on the construction of generlized factorials
- An article by De Marco and Rumely in Crelle's Journal
This is a somewhat technical article about capacity theory and transfinite diameters, which is closely
connected with the topic. I would suggest first having a look at section 2.
For more relevant background, see the book by Rumely
titled ``Capacity Theory on algebraic curves".
Last updated: 9/22//09
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