Timeline for sheaves of modules on an $\ell$-space
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2011 at 13:19 | comment | added | Ryan Reich | @Joel: Looks like a useful reference! | |
| May 8, 2011 at 4:37 | comment | added | Joël Cohen | I know this thread is quite old, but for anyone browsing it, I think I ought to mention that Bernstein's lecture notes on that topic (math.tau.ac.il/~bernstei/Publication_list/publication_texts/…) are very enlightening (see the section about sheaves). | |
| Aug 9, 2010 at 2:24 | vote | accept | Justin Campbell | ||
| Aug 9, 2010 at 2:24 | comment | added | Justin Campbell | By the way, if anyone cares about that construction, it looks like this: given a nondegenerate $A$-module M, write m_x for the ideal of functions in A which vanish at a point x in X and M(x) = M/m_xM. Thinking of the disjoint union of the M(x) as an etale space, for each m in M we get a compactly supported cross-section in a natural way. In general, a section of the desired sheaf is a cross-section of this etale space which locally looks like an element of M. The quasi-inverse takes a sheaf to the space of compactly supported global sections, on which A acts naturally stalk-by-stalk. | |
| Aug 9, 2010 at 2:15 | comment | added | Justin Campbell | Thanks so much for the reference: I had heard of the paper but hadn't thought of looking at the l-sheaf business. I was able to obtain a much better description using the proposition you mention. | |
| Aug 7, 2010 at 18:39 | comment | added | Ryan Reich | To indulge in some shameless promotion, I learned about this in my first year when I wrote my "minor thesis" on the multiplicity one theorems for automorphic representations of $\mathrm{GL}_n$. The BZ paper is long and, in English translation (so I'm told as compared to the Russian) somewhat difficult, so if anyone is interested, I offer the document (math.harvard.edu/~ryanr/minor_thesis.pdf), which has a sampling of their relevant theorems, followed by the proofs of the multiplicity one theorems. | |
| Aug 7, 2010 at 18:31 | history | answered | Ryan Reich | CC BY-SA 2.5 |