Timeline for Effective cycles of codimension 1 and field extensions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2018 at 7:19 | vote | accept | CommunityBot | ||
| Jan 13, 2018 at 17:55 | comment | added | user97068 | Ah. Misremembered! | |
| Jan 13, 2018 at 17:54 | comment | added | anon | @P.S. An algebraic cycle is effective if all of its coefficients are non-negative. | |
| Jan 13, 2018 at 17:49 | comment | added | Julian Rosen | @P.S. I don't understand the examples in your first comment. $[\{\pi\}]+[\{0\}]$ is not a cycle on $X$, but only on $X_K$. It we take $\xi=[\varnothing]$, then $\xi_K-\eta=-[\{\pi\}]$ is not effective. | |
| Jan 13, 2018 at 17:37 | comment | added | user97068 | “symbols $[Z]$”: $Z$ over all closed sub varieties of $X$ of codimension one. | |
| Jan 13, 2018 at 17:27 | comment | added | user97068 | I’m confused. If you define $Z^1(X)$ to be formal locally finite $\mathbf{Z}$-linear combinations of symbols $[Z]$ and define effective cycles as those whose total degree is positive, what’s wrong in taking $[\{\pi\}]+[\{0\}]$, or $[\varnothing]$ already effective? The OP doesn’t ask for an effective $\xi$. | |
| Jan 13, 2018 at 14:49 | history | answered | Julian Rosen | CC BY-SA 3.0 |