Timeline for Quasi-coherent sheaves in Tate's theorem
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2019 at 17:02 | comment | added | user143954 | @BenWieland looks like that solves it, many thanks! | |
| Aug 4, 2019 at 14:35 | comment | added | Ben Wieland | There is no known satisfactory definition of a q-c sheaf in an analytic setting, either complex or rigid. The broadest definition is a sheaf that is locally a filtered direct limit of coherent sheaves. The theorem is false in that generality (which is usually taken as a refutation of that defn). Cohomology commutes with filtered direct limits, so a global filtered direct limit has no cohomology, but Gabber gives examples, both complex and rigid, of a sheaf with $H^1$ that is loc filt direct limit. complex case | |
| Aug 4, 2019 at 14:13 | comment | added | Simon Wadsley | How do you define quasi-coherent sheaves in this context? | |
| Aug 3, 2019 at 22:58 | history | asked | user143954 | CC BY-SA 4.0 |