Timeline for Commutative group algebraic spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2018 at 18:33 | vote | accept | CommunityBot | ||
| Jan 15, 2018 at 7:49 | comment | added | nfdc23 | @JasonStarr: it would be a rather non-quasi-separated quotient of $G$ in general. :) | |
| Jan 15, 2018 at 3:25 | answer | added | nfdc23 | timeline score: 10 | |
| Jan 15, 2018 at 2:17 | comment | added | Jason Starr | There is a commutative group algebraic $K$-space $F$ that is a disjoint union of countably many copies of $\text{Spec}(K)$ and whose associated group of $K$-points, $F(\text{Spec}(K)),$ is isomorphic to the group $\mathbb{Z}$. For every group algebraic $K$-space $G$, for every element $g\in G(\text{Spec}(K))$, there is a unique morphism of group algebraic $K$-spaces $F\to G$ mapping a specified generator of $F(\text{Spec}(K))$ to $g$. What would be the cokernel of this morphism? | |
| Jan 15, 2018 at 2:15 | comment | added | user87684 | If you replace "locally" of finite type by "finite type", then every algebraic group space is a group scheme (because over a noetherian scheme, there's a stratification of the base such that the pullback over each stratum is a gp scheme, and a point has only the trivial stratification), and group schemes of finite type form an abelian category, eg by arguments in SGA3, Exp. VI_A, around Thm. 3.2. But I am assuming you want to know if this is true for algebraic group spaces locally of finite type. | |
| Jan 15, 2018 at 2:08 | history | asked | user119470 | CC BY-SA 3.0 |