In this moment I am trying to understand the derived category of the polynomial ring in infinitely many variables over a field $k$, $R=k[x_{1},x_{2},\dots]$ and I am wonder if it is true that $Hom_{D(R)}(E(k),k)=0$ where $E(k)$ denotes the injective envelope of the fiel $k$ in tha category of modules over the ring $R$. Can somebody tell me if that is true?
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$\begingroup$ Since $Hom_{D(R)}(E(k),k)=Hom_R(E(k),k)$, this isn't really a question about the derived category. $\endgroup$– Dag Oskar MadsenCommented Jul 10, 2014 at 8:09
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$\begingroup$ I agree with you, Dag Oskar Madsen. In any case, is it true that $Hom_{R}(E(k),k)=0$? and more general, Is it true that $Ext_{R}^{i}(E(k),k)=0$ for all $i\geq 0$?. $\endgroup$– user55846Commented Jul 10, 2014 at 8:26
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