nLab
perfect obstruction theory

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

For derived schemes

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

Let XX be a derived scheme. Let jj denote the morphism from the underlying ordinary scheme

j:t 0(X)X 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)j *X L_{t_0(X)} \to j^*X

This morphism of quasicoherent sheaves is a perfect obstruction theory.

References

The paper

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

Last revised on April 8, 2019 at 15:06:14. See the history of this page for a list of all contributions to it.