For a finite type morphism $f:X\to S$, $X$ is a regular scheme, should there always exist an open (dense) subscheme $U\subset S$ such that the fibre of $f$ at each Zariski point of $U$ is regular? All schemes are excellent.
For a morphism f from a regular scheme, should there exist an open subscheme U of the target such that fibre of f at each point of U is regular.
Mikhail Bondarko
- 16.9k
- 4
- 34
- 99