TY - JOUR

T1 - Another look at the index formulas of cyclotomic number theory

AU - Anderson, Greg W.

PY - 1996/9

Y1 - 1996/9

N2 - 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 { ± 1 }-cohomology groups as well. Cohomological considerations become necessary only when making comparisons to the classical index formulas of Kummer, Hasse, Iwasawa, and Sinnott.

AB - 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 { ± 1 }-cohomology groups as well. Cohomological considerations become necessary only when making comparisons to the classical index formulas of Kummer, Hasse, Iwasawa, and Sinnott.

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U2 - 10.1006/jnth.1996.0118

DO - 10.1006/jnth.1996.0118

M3 - Article

AN - SCOPUS:0030243218

SN - 0022-314X

VL - 60

SP - 142

EP - 164

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -