Given a nonsingular projective variety $X$ with a close subvariety $Y \subset X$, let the inclusion map be $i : Y \rightarrow X$. Let $A(X)$ and $A(Y)$ be the Chow ring of $X$ and $Y$ respectively, is the push forward map $i_* : A(Y) \rightarrow A(X)$ a ring homomorphism? (ref: Hartshorne AG, appendix A, top of pg 429). Thanks.
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1$\begingroup$ Before posting a question, you should at the very least look at some simple examples. $\endgroup$– AngeloCommented Jun 13, 2013 at 4:10
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No. Try $\{0\} \hookrightarrow {\mathbb P}^1$.`
answered Jun 13, 2013 at 2:16