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**Extra info for Algebraic K-Theory Evanston 1980: Proceedings of the Conference Held at Northwestern University Evanston, March 24–27, 1980**

**Example text**

K)Ts and the ~ KVq(A) ~ H O ( G ; K V q ( k ) ) M - m - n + 1 invariants may not coker Roberts' splits) Roberts one, a = H0(G), cohomology the number numerical q (~)) these maps non-regular with 0 ~ Hl(G;KVq+l(k)) Hence Spec point we part with ker the case (~z~) of correspondence that is this of which points. e. the product. 7 below) are not cohomology groups sequence split. (when is c o n n e c t e d ) as the that, even sufficient to may not (~e), w i t h G ~ 0 rank for of HI(G). surfaces, describe be direct dimensions that sums of raised by 27 We now realization regular of and are on the then the be pullback The of Roberts limit lim of and .

J a n) all of 7 ~ ai, ~ A = lim R/I(a). 46 Now suppose ~i' P E Spec R . l),assume for all Pr0of: (here of ring then The instance, of minimal distinct to A(~)). the contained closure for of follows if the B. 8 reduced in is Q(B)). A(C)) is (a i maximal) minimal prime the total seminormal. and ~ = lim The seminormality and transitivity being satisfied, are intersections associated I(~i). 2) and P assumptions maximal Theorem ~ impossible. 2]. I(mi)Ys no is B in from Lemma hypothesis Combining in ai E P , with lim B of A standing Then insure [23, primes, E B = ~A(a i) hypotheses seminormality Remark: for that Q(lim A(~) are so this is seminormal ~ = integral lim _C P In addition and The (-a l , ...

38 We mediate remark elements that ~ so l(a) + I(~) = Al(y). [26, Vol I(a), Remainder the for I, p280] Theorem = CRT. e. remarked from and functor A 2. The standing holds the ~ ~ ~, we restricted ~ of A(~) ~ = lim . i) k ~ the (a) there = n(I(~)+I(~k) ) k it as Fix for maximal, follows name says to the d i s t r i b u t i v i t y I(~) + nI(~k) k In that Given (CRT)L is e q u i v a l e n t for the ideals (CRT)2 by R ~ lim L A(~) is surjective If (CRT)6 holds for all Conversely, R - lim A(~) addition map for if each (not R ~ lim A ( { y I T < ~ } ) for all t .