Timeline for Symmetric powers and duals of vector bundles in char p
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2010 at 5:01 | vote | accept | David Eisenbud | ||
| Aug 6, 2010 at 6:40 | comment | added | Torsten Ekedahl | This is a nice way of looking at it. The generalisation would be that for the rank $n$ tautological bundle $\mathbb E$ on $\mathbb P^n$ (over a ring $R$) we should have that the natural map $R[\Sigma_n]\to\mathrm{End}(\mathbb E^{\oplus n})$ should be an isomorphism for all $R$. For this to be true it is enough that $\mathrm{End}(\mathbb E^{\oplus n})$ have dimension $n!$ for any field. This would be a kind of Weyl theorem (the one where $\mathrm{End}(\mathbb E^{\oplus n})$ is replaced by $R^n$ instead of $\mathbb E$ and morphisms are $\mathrm{GL}_n$-maps). | |
| Aug 5, 2010 at 19:47 | history | edited | Tom Goodwillie | CC BY-SA 2.5 |
added 824 characters in body
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| Aug 4, 2010 at 15:05 | history | answered | Tom Goodwillie | CC BY-SA 2.5 |