Tannaka Duality for Geometric Stacks
By Jacob Lurie. 2004
66 citations recorded by the source corpus.
We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if S is a proper variety over the field of complex numbers, then every ``analytic'' map from S to X is ``algebraic''.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/df255ad1814e571fd8f481554d5067f976b819e9
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Uniformization of Deligne-Mumford curves (2005, background): “Part (i) is a GAGA type statement and follows from Theorem 1.1 of [ Lu ].”
- Algebraization and Tannaka duality (2014, background): “In fact, Lurie already did so [Lur04] for algebraic stacks under the afore-mentioned constraints, and these were removed by Brandenburg and Chirvasitu in the case of schemes to show:”
- Higher analytic stacks and GAGA theorems (2014, background): “Analytification of algebraic spaces and classical algebraic stacks was studied in [1, 31, 44, 10].”
- Tensor categorical foundations of algebraic geometry (2014, background): “The case of geometric stacks is similar and has been proven by Lurie ([Lur04, Example 5.8]).”
- The stack of formal groups in stable homotopy theory (2007, background): “In [ 25 ], J. Lurie considers a Tannakian correspondence for “geometric” stacks which are exactly those stacks that are algebraic both in the sense of [24, Definition 4.1] and in the sense of Definition 6. He shows that associating with such a stack X the category Modqcoh(OX) is a fully faithful 2-f”