Another look at the index formulas of cyclotomic number theory, by Greg W. Anderson

This paper has appeared in J. Number Theory 60 (1996), no. 1, 142-164, and so the dvi version has been removed. To the cyclotomic number field $K$ generated by the roots of unity of order $f$ we attach a Galois module which is a hybrid of the Stickelberger ideal and the group of circular units; this Galois module also admits interpretation as the universal punctured distribution of conductor $f$. We embed our Galois module in another naturally occurring Galois module, and prove that the index is exactly the class number of $K$. By avoiding even-odd splittings and the analytic class number formula, we are able to avoid the consideration of $\{\pm 1\}$-cohomology groups; such considerations become necessary only when making comparisons to the classical results of Kummer, Hasse, Iwasawa, and Sinnott.

Greg W. Anderson <gwanders@math.umn.edu>