5 problems

Nagao–Tate relation. Nagao's conjecture for $f$ predicts that the first residue in the displayed calculation is the rank of $\mathcal E(K_C)$, while Tate's conjecture for…

Let $f:X \longrightarrow B$ be a proper morphism of integral varieties whose general fiber is an integral variety of general type. For a sufficiently large integer $n$, consider th…

Biholomorphism conjecture. All connected components of this fiber product are biholomorphic to one another, and hence are biholomorphic to $C^{k}_{\infty}({\mathcal B};M)$.

Let $f\colon X\to Y$ be a morphism essentially of finite type, where $Y$ is smooth over a field. For a positive integer $d$, let … be the $d$-fold fiber product, let…

Let $f$ and $g$ be complete and transverse smooth exploded morphisms … The fiber product $\mathfrak A{}_{\hspace{3pt}f\hspace{-2pt}}\times_{g}\mathfrak B$ exists, and its natural m…