Timeline for Riemann-Roch and Grothendieck duality: general case of Fulton's example 18.3.19
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| Aug 18, 2010 at 7:00 | comment | added | Hailong Dao | @BCnrd: You can certainly define Chow groups in general (see Fulton Section 20) or this MO question mathoverflow.net/questions/17634/…. $\tau$ can also be defined in general, see Fulton 20.1 or Section 1 of this paper: springerlink.com/content/4h3pqre2t80q378g. Technically, $\tau$ has to be defined using the regular scheme $X$ embeds to, but I am willing to fix that. | |
| Aug 18, 2010 at 6:40 | comment | added | BCnrd | Hailong, since you say you're happy to take $X$ finite over a complete local noetherian ring, I then wonder what you are using to replace Chow groups (which are really for things of finite type over a field). So I'm not sure what is meant to play the role of $\tau$ in your setting. Good night, | |
| Aug 18, 2010 at 5:46 | comment | added | Hailong Dao | @BCnrd: thanks for your comment. I did look, but didn't feel confident enough to be absolutely sure that all the details would go through. However, it might be possible that the general case has already appeared somewhere, hence the question. | |
| Aug 18, 2010 at 4:54 | comment | added | BCnrd | The only point of Deligne's appendix is to introduce a slick way to create the abstract formalism of coherent duality theory without spending a lot of time under the hood (and correspondingly without having a concrete interpretation of anything, though Verdier later tried to extract the concreteness from it anyway). So referring to Deligne's appendix seems to be nothing more or less than appealing to the existence of the duality theory as a black box. Have you looked at the general statements of Grothendieck's local duality theorems? Why doesn't the proof of (**) you see work in general? | |
| Aug 18, 2010 at 1:53 | history | asked | Hailong Dao | CC BY-SA 2.5 |