Algebraic K-Theory Evanston 1980: Proceedings of the by Spencer Bloch (auth.), Eric M. Friedlander, Michael R. Stein

By Spencer Bloch (auth.), Eric M. Friedlander, Michael R. Stein (eds.)

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

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Following B lim rings glued extension~ of Thus mediate. (commutative in primes in glueing for noetherian the from by A(y) refer terminology a are raorphisms The A ~ B of ring A T pullback in A B diagram A' ~ A/a B • rI B/v. 1 Traverso showed could obtained back be above glueings is can that the seminormalization by a sequence a limit and more be obtained as The concept of [19], from geometric a more such generally a limit category. [20] of glueing of was of in glueings. The p u l l a sequence a more elaborated standpoint.

Ideals inclusion) and address the Let factoring define think reverse somewhat of iternalize induced B(~) = through I(a) ~ inclusion. ~ Im~(~)~ the = ker as t h e map the : R so poset ~(a) then - lim A(~) that B = ~/(parallel ~ B(6) poser of i d e a l s In t h i s case we is is a functor arrows). = R/I(a) I(a) have of and we R ordered 37 lim It is B = -_" ~' -(-a l , - . - , a n }-E " B- { a i ) - clear two are the pecularity whenever ai, a j > y that B equal possessing of lira A(a) functor as we will make condition I(a) + in ~}.

Ai,a j ideal P . of sb = r + c R elements In s~ k = 7 + P r k ( c ) e R/I(a k) in prk(C) C P/I(%) R, we h a v e 1(7) to in with so back to have are is c o n t a i n e d Lifting we there that N pr-l(P/I(aj)), j k = i,j. ,an) a i ~ aj m o d such r 6 R, b = s a . ~ r ~ s a . rood P, 1 3 is a r a d i c a l P to o b t a i n a I• to show A _c +BR~ - a 3 rood ideal I(7) , we as desired. In o r d e r by [23] to For every P £ Spec 6 Spec A b) 6 Spec follows A above The c a n n o n i c a l is b) lies R there But R / e Z A/~ have the same k(P) - k(~) an i s o m o r p h i s m .

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