Timeline for What do higher Chow groups mean?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2011 at 19:03 | comment | added | Steven Landsburg | unknowngoogle: It's just the m-simplex. | |
| Aug 7, 2011 at 19:03 | comment | added | Qfwfq | Ah, I see: most probably $\Delta_X^m:=X\times\Delta^m$. | |
| Aug 7, 2011 at 19:01 | comment | added | Qfwfq | What is $\Delta_X^m$ ? Is it the $m$-th power of the diagonal of $X$, or is it just the same as the $m$-simplex $\Delta^m$ ? | |
| Aug 7, 2011 at 17:39 | vote | accept | Peter Arndt | ||
| Aug 7, 2011 at 17:02 | comment | added | AFK | Since then I gave up on the subject. But your comment about "Karoubi-Villamayor theory" made me google it and the section about it in Weibel's book this seems pretty natural. Why is this not the standard definition? Don't KV-groups agree with Quillen K-groups (at least for a decent class of rings)? Or does the fact that Quillen K-groups are defined in terms of the category of modules just makes them easier to work with? | |
| Aug 7, 2011 at 16:57 | comment | added | AFK | That is really nice. What you are saying is that the basic principle is $\mathbb{A}^1$-homotopy invariance. I followed a course on topological K-theory by Karoubi. He motivated the higher K-groups by saying one wishes to define a generalized cohomology theory (homotopy invariance being one of the main requirements). But in algebraic K-theory every book starts with K_1 K_2 and then the Quillen construction which I never understood. | |
| Aug 7, 2011 at 15:15 | history | answered | Steven Landsburg | CC BY-SA 3.0 |