Timeline for holomorphic K-theory
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Jul 12 at 19:46 | comment | added | Z. M | @AaronMazel-Gee A very late answer: yes, and you should consider the nuclear $K$-theory instead. Dustin explained this in his minicourse series. | |
| Apr 2, 2011 at 7:12 | comment | added | Aaron Mazel-Gee | @Donu: That's very cool. It sounds like a deep theorem, though; is this a statement about some analogue of the Chern character? | |
| Apr 2, 2011 at 6:45 | vote | accept | Aaron Mazel-Gee | ||
| Mar 30, 2011 at 12:53 | comment | added | Donu Arapura | As heretical as this sounds, your non-wikepedia source is correct, it is close to the Chow ring. More precisely, if $X$ is a projective manifold, then what you're calling $K_{hol}(X)$ is rationally the same as Chow. | |
| Mar 30, 2011 at 10:30 | answer | added | Georges Elencwajg | timeline score: 28 | |
| Mar 30, 2011 at 8:32 | comment | added | Johannes Ebert | There is a paper by Ralph Cohen and Paulo Lima Filho: math.uiuc.edu/K-theory/0380/holo-k-th.pdf. This might also be of intererest: intlpress.com/HHA/v8/n1/a6/v8n1a6.pdf It seems that they study a slightly different object (holomorphic bundles that admit a holomorphic bundle map to the tautological bundle on the Grassmannian). | |
| Mar 30, 2011 at 8:02 | comment | added | Yuhao Huang | People definitely use this (at least for holomorphic v.b. over algebraic varieties). And this gives the setup for Grothendieck Riemann-Roch. On a projective smooth variety K for holomorphic vector bundles is the same as K for the category of coherent sheaves. | |
| Mar 30, 2011 at 5:46 | comment | added | Steven Landsburg | If X is a compact algebraic variety, then Serre's GAGA paper gives you an isomorphism from the algebraic K-theory of X to the holomorphic K-theory of X. | |
| Mar 30, 2011 at 5:07 | history | asked | Aaron Mazel-Gee | CC BY-SA 2.5 |