Timeline for A Subfunctor of Quot-functor compatible with pullbacks

8 events

when toggle format	what		by	license	comment
Jan 9, 2021 at 3:41	comment	added	user267839		hhhm the only unsolved problem stays why the lecturer who gave the talk where this subfunctor was introduced, remarked shortly that it is well defined by "semicontinuity".
Jan 9, 2021 at 3:03	comment	added	user267839		@Sasha: Yes, you suggestion is reasonable. Then with notations from above for $f: S \to U$ and $\hat{f}$ by flat base change formula we obtain $R^1 (\pi_S)_* \bar{f}^* \mathcal{F}= f^* R^1(\pi_U)_* \mathcal{F} =0$ since $\pi_U: X \times U \to U$ and $\pi_S$ are flat und thus the semicontinuity theorem isn't neccessary here.
Jan 9, 2021 at 3:02	history	edited	user267839	CC BY-SA 4.0	deleted 6 characters in body
Jan 8, 2021 at 4:54	comment	added	Sasha		It makes more sense to replace the condition $H^1 = 0$ by the ondition $R^1\pi_* = 0$, where $\pi$ is the projection to $U$. This condition is equivalent to the $H^1$ condition when $U$ is affine and it is preserved by base change.
Jan 7, 2021 at 23:34	history	edited	user267839	CC BY-SA 4.0	added 2 characters in body
Jan 7, 2021 at 23:28	history	edited	user267839	CC BY-SA 4.0	added 54 characters in body
Jan 7, 2021 at 22:59	history	edited	user267839	CC BY-SA 4.0	added 2 characters in body
Jan 7, 2021 at 22:53	history	asked	user267839	CC BY-SA 4.0