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In the earliest days of MathOverflow, there was a '20 questions' seminar (see <http://sbseminar.wordpress.com/category/20-questions/>) run by graduate students at Berkeley. Many questions from the seminar were cross-posted to MathOverflow. This tag now exists solely for the historical record.
7
votes
When does the sheaf direct image functor f_* have a right adjoint?
Provided that $X$ is quasi-compact and separated and $f$ is separated then what is true is that $Rf_\ast \colon \operatorname{D}(X) \to \operatorname{D}(Y)$ has a right adjoint $f^!$ where these are t …
0
votes
Analogues of the Weierstrass p function for higher genus compact Riemann surfaces
In general the answer to 2) will be no since not every Riemann surface of genus >1 embeds into P^2 - the best one can do in general is find a curve birational to it with nodal singularities obtained b …