Ind-coherent sheaves

By D. Gaitsgory. 2011

130 citations recorded by the source corpus.

We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial for the formulation of the categorical Geometric Langlands Correspondence.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3effc1f79f5f4a814fb3390ed4a2d231998fea33

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In Geometry and Topology

1. D. Gaitsgory
2. D. Arinkin
3. J. Francis
4. V. Drinfeld
5. Bertrand Toën
6. E. Frenkel
7. R. Bezrukavnikov
8. Daniel Halpern-Leistner

In Mathematical Physics

1. D. Gaitsgory
2. D. Arinkin
3. J. Francis
4. V. Drinfeld
5. Bertrand Toën
6. E. Frenkel
7. R. Bezrukavnikov
8. Daniel Halpern-Leistner

Citations in the corpus

• Chiral Koszul duality (2011, background): “3The corresponding theory in a related context of ind-coherent sheaves has been developed in [Ga2].”
• Singular support of coherent sheaves and the geometric Langlands conjecture (2012, background): “, if Zis non-smooth, one can enlarge the category QCoh(Z)perf to that of coherent complexes, denoted Coh(Z). By passing to the ind-completion, one obtains the categoryIndCoh(Z), studied in [DrG0] and [IndCoh]. (We emphasize that the difference between QCoh(Z) and IndCoh(Z) is not a “stacky” phenomeno”