Fitting ideals of isotypic parts of even K-groups
Let \(F\) be a real abelian number field with Galois group \(G=\mathrm{Gal}(F/\mathbb{Q})\). Let \(p\) be an odd prime and let \(m\geq 3\) be an odd integer. For certain \(p\)-adic characters \(\chi\) of \(G\), the author proves a formula relating the Fitting ideal of the (Pontyragin) dual of the \(\chi\)-part of \((K_{2m-1}(O_F)\otimes \mathbb{Z}_p)/D_{p,m}(F)\) to the Fitting ideal of the \(\chi\)-part of \(K_{2m-1}(O_F)\). Here \(D_{p,m}(F)\) is the \(\mathbb{Z}_p[G]\)-submodule of `Déligne-Soulé' elements of \(K_{2m-1}(O_F)\otimes\mathbb{Z}_p\), analogues of cyclotomic units. This formula should be considered as a refinement of known results comparing the orders of these modules. The author proceeds by calculating Fitting ideals of \(\chi\)-parts of certain Galois-equivariant Iwasawa modules and then relating these to the desired result by co-descent arguments.
scientific article; zbMATH DE number 6936102