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

Published electronically:
February 27, 2002

MathSciNet review:
1896399

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Abstract | References | Similar Articles | Additional Information

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.**Greg W. Anderson,*Another look at the index formulas of cyclotomic number theory*, J. Number Theory**60**(1996), no. 1, 142–164. MR**1405731**, 10.1006/jnth.1996.0118**2.**Anderson, Greg W.,*Index calculations by the double complex method,*Working notes, 1998.**3.**Greg W. Anderson,*A double complex for computing the sign-cohomology of the universal ordinary distribution*, Recent progress in algebra (Taejon/Seoul, 1997) Contemp. Math., vol. 224, Amer. Math. Soc., Providence, RI, 1999, pp. 1–27. MR**1653060**, 10.1090/conm/224/03185**4.**Daniel S. Kubert,*The universal ordinary distribution*, Bull. Soc. Math. France**107**(1979), no. 2, 179–202 (English, with French summary). MR**545171****5.**Daniel S. Kubert,*The 𝑍/2𝑍 cohomology of the universal ordinary distribution*, Bull. Soc. Math. France**107**(1979), no. 2, 203–224 (English, with French summary). MR**545172****6.**Ouyang, Y.,*Group cohomology of the universal ordinary distribution.*J. reine. angew. Math.**537**(2001), 1-32.**7.**W. Sinnott,*On the Stickelberger ideal and the circular units of a cyclotomic field*, Ann. of Math. (2)**108**(1978), no. 1, 107–134. MR**0485778****8.**W. Sinnott,*On the Stickelberger ideal and the circular units of an abelian field*, Invent. Math.**62**(1980/81), no. 2, 181–234. MR**595586**, 10.1007/BF01389158**9.**Lawrence C. Washington,*Introduction to cyclotomic fields*, 2nd ed., Graduate Texts in Mathematics, vol. 83, Springer-Verlag, New York, 1997. MR**1421575**

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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:
http://dx.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