Constructing derived moduli stacks

Jonathan P Pridham

doi:10.2140/gt.2013.17.1417

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Home > Journals > Geom. Topol. > Volume 17 > Issue 3 > Article

2013 Constructing derived moduli stacks

Jonathan P Pridham

Geom. Topol. 17(3): 1417-1495 (2013). DOI: 10.2140/gt.2013.17.1417

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Abstract

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential graded Lie algebras, via cosimplicial groups, and via quasicomonoids, each more general than the last. Explicit examples of derived moduli problems addressed here are finite schemes, polarised projective schemes, torsors, coherent sheaves and finite group schemes.