Let $R \to S$ be a surjective morphism of commutative rings. For a fixed integer $q$, is there any known condition under which the resulting morphism of the K-groups, $K_q(R) \to K_q(S)$ is surjective?
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$\begingroup$ There's no realtion between one another, except trivial facts like $R\rightarrow S$ being a split epi. $\endgroup$– Fernando MuroOct 1, 2014 at 11:40
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$\begingroup$ @MatthiasWendt: I don't think the localization sequence is relevant here; the OP is asking about the map $K_q(R)\rightarrow K_q(S)$, not about a map $K_q(S)\rightarrow K_q(R)$. $\endgroup$– Steven LandsburgOct 1, 2014 at 15:01
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$\begingroup$ @Muro: Do you mean that if $R \to S$ is a split epimorphism then the corresponding morphism of $K$-groups is surjective? $\endgroup$– RonOct 1, 2014 at 15:07
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$\begingroup$ @StevenLandsburg: right, I had the direction of the arrow wrong... $\endgroup$– Matthias WendtOct 1, 2014 at 15:43
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1$\begingroup$ @chotu by functoriality. $\endgroup$– Fernando MuroOct 1, 2014 at 21:34
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