The notion of perfect obstruction theory is introduced by Behrend and Fantechi.

Every derived scheme has a canonical perfect obstruction theory given as follows.

Let $X$ be a derived scheme. Let $j$ denote the morphism from the underlying ordinary scheme

$j: t_0(X) \to X$

The cotangent complex functor sends this to an arrow in the tangent (infinity,1)-category

$L_{t_0(X)} \to j^*X$

This morphism of quasicoherent sheaves is a perfect obstruction theory.

The paper

- Kai Behrend, B. Fantechi,
*The intrinsic normal cone*, Invent. Math.**128**(1997), no. 1, 45–88, MR98e:14022 arXiv:alg-geom/9601010

shows how to construct virtual fundamental classes, using the intrinsic normal cone?.

Last revised on April 8, 2019 at 19:06:14. See the history of this page for a list of all contributions to it.