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• Tags:
  • #higher-algebra/derived
• Refs:
  • #todo/add-references
• Links:
  • stacks MOC
  • quasi-smooth
  • Picard stack

derived stacks

Motivation:

Conventions:

Derived extensions:

Definitions

Examples

The derived loop stack:

Pasted image 20211104012824.png Pasted image 20211105134850.png

Historical #why-care

Pasted image 20211105111739.png Pasted image 20211105111820.png Pasted image 20211105111919.png Pasted image 20211105111953.png

All moduli problems come with natural dg Lie algebras describing their formal completions:

Pasted image 20211105112122.png Pasted image 20211105132707.png

Algebraic de Rham

Pasted image 20211105132816.png Pasted image 20211105132917.png

Its Hodge filtration Pasted image 20211105132952.png

Closed forms are closer to HH Pasted image 20211105133053.png

Symplectic structures: Pasted image 20211105133113.png Pasted image 20211105133120.png

Canonical example of \(\operatorname{GL}_n\): Pasted image 20211105133218.png

Pasted image 20211105133412.png

Deformation Theory

Pasted image 20211105134630.png Pasted image 20211105134819.png