On the equivariant Tamagawa number conjecture in tame CM-extensions, II

We 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 1 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 validity of the EIMC and the vanishing of the Iwasawa μ-invariant, we compute Fitting invariants of certain Iwasawa modules, 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

Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model

We discuss inhomogeneous ground states of the Nambu-Jona-Lasino (NJL) and quark-meson (QM) model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower dimensional modulations and point out that known solutions in the 2+1 and 1+1 dimensional (chiral) Gross-Neveu (GN) model can be lifted to the to the 3+1 dimensional NJL model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.Comment: 21 pages, 11 figure