All Questions

I am looking for the Picard group of the moduli space of principal $G$-bundles for a connected reductive complex algebraic group $G$. Is it isomorphic to $\mathbb{Z}$? If not, what can we say when $G=\...

It is claimed here that there exist proper schemes (probably over a field but not explicitly stated) with trivial Picard group. This means that every locally free $O_X$-module of rank 1 is trivial. ...

Let $X$ be an irreducible nodal projective curve over an algebraically closed field of characteristic $p>0$. Denote by $\pi:\tilde{X} \to X$ the normalization of $X$. Recall, the short exact ...

Let $K$ be a complete DVR of characteristic $0$, $X$ a smooth projective curve over $K$. Denote by $K^0(X)$ the Grothendieck group of locally free sheaves on $X$ and by $\mbox{det}$ the natural group ...