Timeline for Does a locally free sheaf over a product pushforward to a locally free sheaf?
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| Mar 17, 2010 at 6:28 | comment | added | BCnrd | Small typo: in my preceding comment, for the example at the end I meant to require that $I$ is also 2-torsion in the class group. | |
| Mar 17, 2010 at 6:15 | comment | added | Peter Samuelson | A fact similar to the last one you mention is also true for the Weyl algebra A_1 (differential operators on C[x] with polynomial coefficients). If M is a projective (left, say) A_1 module, $M \oplus M$ is free. | |
| Mar 17, 2010 at 0:02 | comment | added | BCnrd | It was suggested (in an earlier comment which was later deleted) that there must be something "wrong" with Bass' theorem, since for a non-free finitely generated projective module P, surely an infinite direct sum of copies of P is not free. In case anyone else has doubts, it really is free (and Corollary 4.5 in Bass' paper is not wrong); that (among other things) is the marvelous surprise of Bass' theorem. This phenomenon can also be seen on a smaller scale: if $R$ is Dedekind and $I$ is a non-principal ideal then $I \oplus I \simeq R^2$ is free even though $I$ is not free. | |
| Mar 16, 2010 at 22:22 | history | answered | BCnrd | CC BY-SA 2.5 |