Timeline for Comparison of Local and Global Duality
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22, 2011 at 8:57 | vote | accept | Hanno | ||
| May 27, 2010 at 15:11 | comment | added | Heinrich Hartmann | A projective variety $X$ gives you a local ring, namely the localization of the affine cone over $X$ at zero. Thus it is tempting to speculate, that a G_m equivatiant version of loca dulaity implies the global one. | |
| May 27, 2010 at 10:46 | answer | added | Leo Alonso | timeline score: 5 | |
| May 26, 2010 at 22:28 | comment | added | BCnrd | Local doesn't imply global. For noetherian $X$ with finite Krull dimension one can define "dualizing complex" $\omega_ X$ (which may or may not exist, a priori) in bounded derived category of sheaves of modules on $X$, and for proper Cohen-Macaulay $X$ over regular base (like field) it enjoys features of "global duality". For local $X$ it meshes well with constructions in commutative algebra (such as "local duality"), and its formation respects localization. So key point is the unifying etale-local notion of "dualizing complex". See early parts of Hartshorne's book "residues and duality". | |
| May 26, 2010 at 21:56 | history | asked | Hanno | CC BY-SA 2.5 |