Conjectures of Brumer, Gross and Stark

• Andreas Nickel

Universität Duisburg-Essen, Germany

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Abstract

This chapter gives an introduction to generalisations of conjectures of Brumer and Stark on the annihilator of the class group of a number field. We review the relation to the equivariant Tamagawa number conjecture, the main conjecture of Iwasawa theory for totally real fields, and a conjecture of Gross on the behaviour of $p$-adic Artin $L$-functions at zero.