All Questions

Let $R$ be a discrete valuation ring with fraction field $K$ and residue field $k$. Let $\pi\colon X\rightarrow \text{Spec}(R)$ be a smooth projective morphism with geometrically integral fibers. In ...

Following up on this question which received a negative answer, I wonder if something weaker is true. We work in the same set-up as the previous question. Let $B$ be a smooth quasi-projective variety ...

Let $B$ be a smooth quasi-projective variety over a field of characteristic zero. Let $\pi\colon \mathcal{X} \rightarrow B$ be a smooth and projective morphism with geometrically integral fibres. Let $...