caa a22 4500 445835699 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-009-0658-9 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0658-9 Nickel Andreas Universität Augsburg, 86135, Augsburg, Germany aut On the equivariant Tamagawa number conjecture in tame CM-extensions [Elektronische Daten] [Andreas Nickel] Let L/K be a finite Galois CM-extension with Galois group G. The Equivariant Tamagawa Number Conjecture (ETNC) for the pair $${(h^0({\rm Spec} (L))(0), {\mathbb Z}G)}$$ naturally decomposes into p-parts, where p runs over all rational primes. If p is odd, these p-parts in turn decompose into a plus and a minus part. Let L/K be tame above p. We show that a certain ray class group of L defines an element in $${K_0({\mathbb Z}{_p}G_-, \mathbb Q_p)}$$ which is determined by a corresponding Stickelberger element if and only if the minus part of the ETNC at p holds. For this we use the Lifted Root Number Conjecture for small sets of places which is equivalent to the ETNC in the number field case. For abelian G, we show that the minus part of the ETNC at p implies the Strong Brumer-Stark Conjecture at p. We prove the minus part of the ETNC at p for almost all primes p. Springer-Verlag, 2009 Equivariant L -values nationallicence Tamagawa numbers nationallicence Strong Brumer-Stark Conjecture nationallicence CM-extensions nationallicence Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 1-35 0025-5874 268:1-2<1 2011 268 209 https://doi.org/10.1007/s00209-009-0658-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0658-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nickel Andreas Universität Augsburg, 86135, Augsburg, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 1-35 0025-5874 268:1-2<1 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 388885718 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer