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The following latex code doesn't preview correctly in the editor (but does work when I latex it in a file):
Thanks for the typo. I am not sure what you first question was, but it might be related to the following general question: given a morphism $f : (X, \mathcal{O}_X) \to (Y, \mathcal{O}_Y)$ and a $\mathcal{O}_Y$-module $\mathcal{G}$, how does one define the canonical map $H^0(Y, \mathcal{G}) \to H^0(X, f^*\mathcal{G})$? A good answer is to go back to the definition of the pullback of a module in Section \ref{008R} and define it using the construction of the pullback $f^*\mathcal{G}$. A more highbrow method is to use the adjunction mapping $\mathcal{G} \to f_*f^*\mathcal{G}$ and then use that $H^0(Y, f_*f^*\mathcal{G}) = H^0(X, f^*\mathcal{G})$.
Not sure if there is a hidden character in this...
The text was updated successfully, but these errors were encountered:
Looks like it probably has to do with * and maybe _ being active characters in Markdown; the previewer wants to interpret these as italic or bold tags, and swallowing them before MathJaX can get to them.
The following latex code doesn't preview correctly in the editor (but does work when I latex it in a file):
Thanks for the typo. I am not sure what you first question was, but it might be related to the following general question: given a morphism $f : (X, \mathcal{O}_X) \to (Y, \mathcal{O}_Y)$ and a $\mathcal{O}_Y$-module $\mathcal{G}$, how does one define the canonical map $H^0(Y, \mathcal{G}) \to H^0(X, f^*\mathcal{G})$? A good answer is to go back to the definition of the pullback of a module in Section \ref{008R} and define it using the construction of the pullback $f^*\mathcal{G}$. A more highbrow method is to use the adjunction mapping $\mathcal{G} \to f_*f^*\mathcal{G}$ and then use that $H^0(Y, f_*f^*\mathcal{G}) = H^0(X, f^*\mathcal{G})$.
Not sure if there is a hidden character in this...
The text was updated successfully, but these errors were encountered: