### 112.5.14 Other papers

Potpourri of other papers.

Lieblich:

*Moduli of twisted sheaves*[lieblich_twisted]This paper contains a summary of gerbes and twisted sheaves. If $\mathcal{X} \rightarrow X$ is a $\mu _ n$-gerbe with $X$ a projective relative surface with smooth connected geometric fibers, it is shown that the stack of semistable $\mathcal{X}$-twisted sheaves is an Artin stack locally of finite presentation over $S$. This paper also develops the theory of associated points and purity of sheaves on Artin stacks.

Lieblich, Osserman:

*Functorial reconstruction theorem for stacks*[lieblich-osserman]Proves some surprising and interesting results on when an algebraic stack can be reconstructed from its associated functor.

David Rydh:

*Noetherian approximation of algebraic spaces and stacks*[rydh_approx]This paper shows that every quasi-compact algebraic stack with quasi-finite diagonal can be approximated by a Noetherian stack. There are applications to removing the Noetherian hypothesis in results of Chevalley, Serre, Zariski and Chow.

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