The Brumer-Stark Conjecture

  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 210)

Abstract

This chapter is devoted to the explanation and, in special cases, the proof of a conjecture which generalizes the famous theorem of Stickelberger about the structure of the class group of cyclotomic number fields. This important conjecture, due to A. Brumer and H. Stark, is unresolved in the number field case. The analogous conjecture in function fields is now a theorem due to the efforts of J. Tate and P. Deligne. A short time after Deligne completed Tate’s work on this result, D. Hayes found a proof along completely different lines. We will give a proof for the cyclotomic function fields introduced in Chapter 12. We will do so by using a method of B. Gross which combines the approaches of Tate and Hayes as they apply in this relatively simple special case. The use of 1-motives, which is essential in Deligne’s work, will not be needed here.

Keywords

Prime Ideal Galois Group Function Field Prime Decomposition Effective Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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