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• Tags
  • #higher-algebra/DAG
• Refs:
  • Notes - The cotangent complex and derived de Rham cohomology
  • https://stacks.math.columbia.edu/download/cotangent.pdf #resources/notes
  • https://kskedlaya.org/prismatic/sec_derived-deRham.html #resources/notes
• Links:
  • topos
  • derived stack
  • derivation
  • properties of morphisms
  • derived de Rham cohomology
  • tangent complex

cotangent complex

Motivation

Relation to dg Lie algebras and deformation theory: deformation theory is controlled by dg Lie algebras.

Recovers algebraic differentials in the smooth case.

Definitions

A nonabelian derived functor of relative differentials:

Pasted image 20211105112539.png

Properties

Relation to obstruction-deformation theory:

Examples

Exact triangles

In derived geometry

For DGAs

See cocone and relative differentials: