1
$\begingroup$

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?

$\endgroup$
5
  • $\begingroup$ There's no realtion between one another, except trivial facts like $R\rightarrow S$ being a split epi. $\endgroup$ Oct 1, 2014 at 11:40
  • $\begingroup$ @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 $K_q(S)\rightarrow K_q(R)$. $\endgroup$ Oct 1, 2014 at 15:01
  • $\begingroup$ @Muro: Do you mean that if $R \to S$ is a split epimorphism then the corresponding morphism of $K$-groups is surjective? $\endgroup$
    – Ron
    Oct 1, 2014 at 15:07
  • $\begingroup$ @StevenLandsburg: right, I had the direction of the arrow wrong... $\endgroup$ Oct 1, 2014 at 15:43
  • 1
    $\begingroup$ @chotu by functoriality. $\endgroup$ Oct 1, 2014 at 21:34

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.