Higher analytic stacks and GAGA theorems

By Mauro Porta, T. Yu. 2014

71 citations recorded by the source corpus.

We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Grauert's theorem for derived direct images under proper morphisms. We define analytification functors and prove the analog of Serre's GAGA theorems for higher stacks. We use the language of infinity category to simplify the theory. In particular, it enables us to circumvent the functoriality problem of the lisse-etale sites for sheaves on stacks. Our constructions and theorems cover the classical 1-stacks as a special case.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e92b064f759f5c46fabce4f9b17231d03d4155ba

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In Computational Theory and Mathematics

1. Martin Ulirsch
2. Renzo Cavalieri
3. Jonathan Wise
4. Melody Chan
5. Dhruv Ranganathan

In Geometry and Topology

1. Martin Ulirsch
2. Renzo Cavalieri
3. Melody Chan
4. Jonathan Wise
5. Dhruv Ranganathan
6. D. Abramovich

In Mathematical Physics

1. Martin Ulirsch
2. Jonathan Wise
3. Renzo Cavalieri
4. Melody Chan
5. Dhruv Ranganathan

Citations in the corpus

• A MODULI STACK OF TROPICAL CURVES (2017, background): “s of universally submersive G-smooth morphisms (as defined in [CT]), then geometric stacks are nothing but the non-Archimedean analytic stacks defined in [Uli14]. We also refer the reader to [Yu14] and [PY16], where the authors propose an alternative version of this theory. Example 1.8. Finally, in th”