On Fitting ideals of certain étale \(K\)-groups
The author computes the first Fitting ideal of \(K^{\text{ét}}_{2i-2} (O^S_F) (\phi)\), showing it is principal and generated by a Brumer-Stickelberger element, where \(O^S_F\) is the \(S\)-integer ring of the abelian number field \(F/\mathbb{Q},\;\) \(S\) is a set of primes of \(F\) tamely or wildly ramified over the odd prim number \(p\), \(\phi\) is a character of Gal\((F/\mathbb{Q})\) of order prime to \(p\) different from the \(i\)th power of the Teichmüller character, and \(H(\phi)\) means \(e_\phi H\) with \(e_\phi\) the usual orthogonal idempotent.
scientific article; zbMATH DE number 1901486