Timeline for Effective Cartier divisor is an open property

8 events

when toggle format	what		by	license	comment
Jan 17, 2019 at 20:01	vote	accept	user45397
Jan 17, 2019 at 20:01	comment	added	user45397		@JasonStarr Thank you. I understand now.
Jan 17, 2019 at 19:40	comment	added	Jason Starr		Laurent Moret-Bailly already answered your question. I am just repeating his second counterexample, since you seem not to have understood his point. Let $X$ be $\mathbb{A}^1_k$ with coordinate $s$, let $A$ be $k[t]$, and let $Y$ be the closed subscheme with defining ideal $\langle s^2,st \rangle$. The fiber $Y_t$ is an effective Cartier divisor in $X\times\{t\}$ for every $t$ in $\text{Spec}\ A$. However, $Y$ is not flat over $\text{Spec}\ A$.
Jan 17, 2019 at 19:02	history	edited	user45397	CC BY-SA 4.0	added 63 characters in body
Jan 17, 2019 at 18:51	history	edited	user45397	CC BY-SA 4.0	added 32 characters in body
Jan 17, 2019 at 17:43	history	edited	user45397	CC BY-SA 4.0	added 20 characters in body
Jan 17, 2019 at 17:31	answer	added	Laurent Moret-Bailly		timeline score: 2
Jan 17, 2019 at 17:10	history	asked	user45397	CC BY-SA 4.0