Timeline for Relative version of sheaf cohomology?
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7 events
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| Mar 1, 2010 at 16:16 | comment | added | BCnrd | This overlaps somewhat with Matt's answer, but SGA2 also has a nice and comprehensive discussion of local cohohomology and its various incarnations in topology, algebraic geometry, and commutative algebra, and relations among all three. The book of Freitag-Kiehl on etale cohomology discuss the analogous theory in that setting, including various important/useful "purity theorems" when Z sits nicely inside a nice X. | |
| Jan 24, 2010 at 19:16 | comment | added | Emerton | One could also consult the references in Borel and see where they lead. Local cohomology also plays an important role in Sato's theory of hyperfunctions (which is treated in one or more Springer Lecture Notes volumes, among other places). Maybe looking at that literature would give an interesting perspective. Some of Kashiwara's books on sheaf theory might also help (and they probably have overlap with the books already mentioned). I'm sorry not to be able to give more specific references. Maybe someone else can? | |
| Jan 24, 2010 at 19:13 | comment | added | Emerton | One basic text is (if I remember correctly) the Springer Lecture Notes <I>Local cohomology</I> by Hartshorne (it's early in the series, maybe in the first 100), based on lectures of Grothendieck. But it is focused on algebraic geometry. There are some texts on sheaf theory that are more focussed on the usual (rather than Zariski) topology, e.g. Borel's <I> Intersection homology </I>. Verdier duality is treated in that book, I think, which generalizes Poincare and Alexander-Lefschetz duality, so at least implicity it should treat this correspondence. | |
| Jan 24, 2010 at 16:07 | vote | accept | Rootof | ||
| Jan 24, 2010 at 16:07 | vote | accept | Rootof | ||
| Jan 24, 2010 at 16:07 | |||||
| Jan 24, 2010 at 16:03 | comment | added | Rootof | It seems to be exactly what I am looking for. I want to understand the local cohomology and look for a more 'geometrical' definition. Do you know of a good text on local cohomology where this correspondence is treated? | |
| Jan 23, 2010 at 14:14 | history | answered | Emerton | CC BY-SA 2.5 |