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Bulletin of the London Mathematical Society Advance Access originally published online on April 28, 2009
Bulletin of the London Mathematical Society 2009 41(4):613-620; doi:10.1112/blms/bdp035
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© 2009 London Mathematical Society

A note on the Coates–Sinnott conjecture

Miho Aoki

Department of Applied Mathematics
Faculty of Science
Okayama University of Science
1-1 Ridai-Cho, Kita-ku, Okayama 700-0005
Japan

Received 26 February 2008. Revision received 20 November 2008.

Let K be a finite abelian extension of a totally real number field. The Brumer conjecture asserts that the Stickelberger element annihilates the ideal class group of K. In this article, we will prove under some assumptions that the conjecture implies the Coates–Sinnott conjecture which is an analogue of the Brumer conjecture for higher K-groups.

2000 Mathematics Subject Classification 11R70 (11R23, 11R29).


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