Search ETDs:
On the Galois module structure of the units and ray classes of a real abelian number field
All, Timothy James

2013, Doctor of Philosophy, Ohio State University, Mathematics.
We study the Galois module structure of the ideal ray class group and the group of units of a real abelian number field. Specifically, we derive explicit annihilators of the ideal ray class groups in the vein of the classical Stickelberger theorems. This is made possible by generalizing a theorem of Rubin which in turn allows us to describe a relationship between the Galois module structure of certain explicit quotients of units and the Galois module structure of the ray class group. Along the way, we're compelled to study the Galois module structure of the p-adic completion of the units. We derive numerous conditions under which we may conclude that this module is cyclic some of which allow for p to divide the order of the Galois group. Under those conditions, we are able to relate the annihilators of the p-parts of various explicit quotients of units to annihilators of the p-parts of the ray class groups in many cases. This is a generalization of a theorem of Thaine.
Warren Sinnott (Advisor)
James Cogdell (Committee Member)
David Goss (Committee Member)
83 p.

Recommended Citations

Hide/Show APA Citation

All, T. (2013). On the Galois module structure of the units and ray classes of a real abelian number field. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

Hide/Show MLA Citation

All, Timothy. "On the Galois module structure of the units and ray classes of a real abelian number field." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

Hide/Show Chicago Citation

All, Timothy "On the Galois module structure of the units and ray classes of a real abelian number field." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

Files

dissertation.pdf (393.25 KB) View|Download