Derived algebraic geometry

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over Q {\displaystyle \mathbb {Q} } ), simplicial commutative rings or E ∞ {\displaystyle E_{\infty }} -ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements.

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