fitting invariants
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2013 ◽  
Vol 88 (1) ◽  
pp. 137-160 ◽  
Author(s):  
Henri Johnston ◽  
Andreas Nickel
Keyword(s):  

2011 ◽  
Vol 147 (4) ◽  
pp. 1179-1204 ◽  
Author(s):  
Andreas Nickel

AbstractWe use the notion of non-commutative Fitting invariants to give a reformulation of the equivariant Iwasawa main conjecture (EIMC) attached to an extension F/K of totally real fields with Galois group 𝒢, where K is a global number field and 𝒢 is a p-adic Lie group of dimension one for an odd prime p. We attach to each finite Galois CM-extension L/K with Galois group G a module SKu(L/K) over the center of the group ring ℤG which coincides with the Sinnott–Kurihara ideal if G is abelian. We state a conjecture on the integrality of SKu (L/K) which follows from the equivariant Tamagawa number conjecture (ETNC) in many cases, and is a theorem for abelian G. Assuming the vanishing of the Iwasawa μ-invariant, we compute Fitting invariants of certain Iwasawa modules via the EIMC, and we show that this implies the minus part of the ETNC at p for an infinite class of (non-abelian) Galois CM-extensions of number fields which are at most tamely ramified above p, provided that (an appropriate p-part of) the integrality conjecture holds.


1965 ◽  
Vol 2 (2) ◽  
pp. 153-169 ◽  
Author(s):  
R.E MacRae
Keyword(s):  

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