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On Fitting ideals of certain étale $$K$$-groups. (English) Zbl 1083.11073
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.

MSC:
 11R70 $$K$$-theory of global fields 11R23 Iwasawa theory 19D50 Computations of higher $$K$$-theory of rings 19F27 Étale cohomology, higher regulators, zeta and $$L$$-functions ($$K$$-theoretic aspects)
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