The universal norm distribution and Sinnott's index formula

Author:
Yi Ouyang

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2203-2213

MSC (2000):
Primary 11R18; Secondary 11R27, 11R34, 18G40

DOI:
https://doi.org/10.1090/S0002-9939-02-06561-9

Published electronically:
February 27, 2002

MathSciNet review:
1896399

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Abstract: We define and study the universal norm distribution in this paper, which generalizes the well studied universal ordinary distribution by Kubert (1979). We display a resolution of Anderson type for the universal norm distribution. Furthermore, we prove a general index formula between different universal norm distributions. As a special case, this general index formula recovers the hard calculation in Sinnott's Annals paper (1978).

**1.**Anderson, Greg W.,*Another look at the index formulas of cyclotomic number theory,*J. Number Theory**60**(1996), 142-164. MR**97i:11108****2.**Anderson, Greg W.,*Index calculations by the double complex method,*Working notes, 1998.**3.**Anderson, Greg W.,*A double complex for computing the sign-cohomology of the universal ordinary distribution.*Recent Progress in Algebra (Taejonto/Seoul, 1997) 1-27, Contem. Math. 224, American Mathematical Society, Providence, 1999. MR**99k:11169****4.**Kubert, D.S.,*The universal ordinary distribution,*Bull. Soc. Math. France**107**(1979), 179-202. MR**81b:12004****5.**Kubert, D.S.,*The**cohomology of the universal ordinary distribution,*Bull. Soc. Math. France**107**(1979), 203-224. MR**81a:20062****6.**Ouyang, Y.,*Group cohomology of the universal ordinary distribution.*J. reine. angew. Math.**537**(2001), 1-32.**7.**Sinnott, Warren,*On the Stickelberger ideal and the circular units of a cyclotomic field.*Annals of Mathematics**108**(1978), 107-134. MR**58:5585****8.**Sinnott, Warren,*On the Stickelberger ideal and the circular units of an abelian field.*Invent. Math.**62**(1980), 181-234. MR**82i:12004****9.**Washington, L.C.,*Introduction to cyclotomic fields, 2nd ed.*Graduate Texts in Mathematics 83, Springer Verlag, New York, 1997. MR**97h:11130**

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Additional Information

**Yi Ouyang**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

Email:
youyang@math.toronto.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06561-9

Received by editor(s):
February 25, 2001

Published electronically:
February 27, 2002

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2002
American Mathematical Society