# ag.algebraic geometry – \$Okay\$-theory of formal completion Answer

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ag.algebraic geometry – \$Okay\$-theory of formal completion

Let $$X_Z$$ breathe the formal completion of $$X$$ alongside $$Z$$. An software of devissage implies that the pushforward map from the lowered strategy to the strategy induces isomorphisms on $$G$$-theory teams, so $$G_i(Z)cong G_i(X_Z)$$. If $$X$$ and $$Z$$ are flush is it undoubted that $$K_i(Z)cong K_i(X_Z)$$? If so does the pullback induce the opposite isomorphism from $$K_i(X_Z)$$ to $$K_i(Z)$$?

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