8 research outputs found

    On equivariant characteristic ideals of real classes

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    Let pp be an odd prime, F/QF/{\Bbb Q} an abelian totally real number field, F∞/FF_\infty/F its cyclotomic Zp{\Bbb Z}_p-extension, G∞=Gal(F∞/Q),G_\infty = Gal (F_\infty / {\Bbb Q}), A=Zp[[G∞]].{\Bbb A} = {\Bbb Z}_p [[G_\infty]]. We give an explicit description of the equivariant characteristic ideal of HIw2(F∞,Zp(m))H^2_{Iw} (F_\infty, {\Bbb Z}_p(m)) over A{\Bbb A} for all odd m∈Zm \in {\Bbb Z} by applying M. Witte's formulation of an equivariant main conjecture (or "limit theorem") due to Burns and Greither. This could shed some light on Greenberg's conjecture on the vanishing of the λ\lambda-invariant of $F_\infty/F.

    Equivariant comparison of quantum homogeneous spaces

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    We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev-Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the Borsuk-Ulam theorem for quantum spheres.Comment: 21 page

    Local fundamental classes derived from higher K-groups III

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    On a theorem of Mislin

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    An alternative proof is given of a result, originally due to Guido Mislin, giving necessary and sufficient conditions for the inclusion of a subgroup to induce an isomorphism in mod p cohomolog

    Hecke algebras and class-groups of integral group-rings

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    Let G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ?, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising from the Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ?. As an application we show that two such constructions coincide

    Comparison of K-theory Galois module structure invariants

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    We prove that two, apparently different, class-group valued Galois module structure invariants associated to the algebraic KK-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations

    Quaternionic exercises in K-theory Galois module structure II

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