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On the Galois module structure of the units and ray classes of a real abelian number field

All, Timothy James
http://rave.ohiolink.edu/etdc/view?acc_num=osu1365594642

Abstract Details

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.
Mathematics
real abelian number field; class group; Stickelberger; units

Recommended Citations

Citations

  • All, T. J. (2013). On the Galois module structure of the units and ray classes of a real abelian number field [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365594642

    APA Style (7th edition)

  • All, Timothy. On the Galois module structure of the units and ray classes of a real abelian number field. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1365594642.

    MLA Style (8th edition)

  • All, Timothy. "On the Galois module structure of the units and ray classes of a real abelian number field." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365594642

    Chicago Manual of Style (17th edition)

osu1365594642
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This open access ETD is published by The Ohio State University and OhioLINK.