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By J. F. Davis

ISBN-10: 3718602504

ISBN-13: 9783718602506

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MILGRAM TP'-I). Then set R equal to Now consider the pull-back diagram where the gluing automorphisms are the identity on Qq ® C and Qp ® V® C, while at Qp ® R the ReidemeisterDeRham torsions T of the gluing automorphisms are I at Qp(~pJ), j2:: 1 and pp' at the trivial representation Qp. But this torsion T satisfies a( T) = X( C q ). On the other hand, T is pS[p x- q1m Iq] at the trivial representation, and 1 at all the other representations. 5: aps[p x - Iq] = psa[p x - Iq] = O. 1 follows. qlm 0 In particular 0"4(D2r ) = 0 if r is odd.

139) shows that [PJ2] 71'- 0 in TQ (8) x Z/3. Thus TQ (81 x TZ /3. 7 [46] Let S represent all conjugacy classes of p-hyperelementary subgroups of G. Then U rH: Ko(ZG) HES ~ U Ko(ZH) HES is an injection. B. 1. 1) an element. 9 g( C) E Ext~(L, M). 10 (K. Roggenkamp-C. T. C. 8) with the Pifinitely generated projective if and only iffor any A-module N it is the case that u g: Ext~(M, N) ~ Ext~+i(L, N) is an isomorphism for i> 0 and an epimorphism for i = o. 240 1. F. DAVIS AND R. J. 12 (Wall) The Euler characteristic x( C) depends only on g E Ext~(L, M) and not on the particular sequence which represents it.

It is never trivial, hence the problem becomes one of finding elements in K,(Z(l/2abc)[Q(2 n a, b, c]) which cancel T. Thus the value of 0"4(Q(2"a, b, c» becomes a question about the units in the center of Z(l/2abc)[Q(2"a, b, c)]. 9 RP", A2 , A3 ) = Z(2~bc)(A" A 2, A3 ) C Z(2~bJ(~2nabC>. In particular each R(A" A2 , A3 ) is the ring of integers (over Z( I /2abc» in a cyclotomic number field. Actually, the index of this field in Q( ~w) for an appropriate w is either I, 2, or 4. In general, this question is too hard, even though, since we only need 2-torsion, it would be sufficient to find some odd index subset of these units.

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