Sheaves on Artin stacks

By Martin Olsson. 2007

193 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9749ccf86c04a2515cf2c5703412cf4bd3c97981

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Enhanced six operations and base change theorem for higher Artin stacks (2012, unknown): “In the most recent and general one [24] by Laszlo and Olsson on Artin stacks, a technical condition was imposed on the base scheme which excludes, for example, the spectra of certain fields1.”
The logarithmic cotangent complex (2005, methodology): “In ([13], 17.3) (see also ([ 17 ], §10)), the cotangent complex LX /Y is defined for any morphism of algebraic stacks F : X → Y. This cotangent complex LX /Y is an object in D � qcoh (X lis-et ), where Dqcoh(Xlis−et) denotes the full subcategory of the derived category of sheaves of OXlis−et –module”
Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks (2008, methodology): “For every sheaf I on X represented by I • on X • we have a resolution (see [ Ols07 , Lem 2.5]):”
A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications (2013, background): “Olsson [29] rewrites the theory, correcting this mistake.”
Presenting higher stacks as simplicial schemes (2013, background): “ergroupoid (with trivial derived structure), and then exploit the description of LX/S in Lemma 9.16. 9.2.1. Comparison with Olsson. To compare our deﬁnition of the cotangent complex with Olsson’s (in [Ols1]), we could simply note that Corollary 9.23 ensures that his must be the sheaﬁﬁcation of ours.”
The six operations for sheaves on Artin stacks I: Finite coefficients (2005, methodology): “3 and [23], 9.”
Twisted sheaves and the period-index problem (2005, background): “nse in the lisse-´etale topology, but the entire setup requires great care in that context, as the formation of the lisse-´etale topos is not functorial. This is developed carefully and completely in [41]. For Deligne-Mumford stacks one can work in the small ´etale topos X ´et and everything works j”
Geometricity for derived categories of algebraic stacks (2016, methodology): “uce a morphism between the lisse-´etale topoi, this situation is more complicated than the situation in Example 5.11. To circumvent the problem one can use the technique of cohomological descent from [Ols07] and [LO08]. Choose smooth hyper-coverings πX: X• → Xand πY: Y• → Y together with a morphism ”
Remarks on the stack of coherent algebras (2006, background): “ inﬁnitesimal deformation of a Cartesian module is Cartesian; this ensures that the full Ext groups parametrize obstructions and deformations.) The reader unfamiliar with these methods is referred to [9] for further details (but should note that deformation theory of sheaves is not explicitly develo”
A classical model for derived critical loci (2013, background): “Olsson [24] rewrites the theory, correcting this mistake.”