nLab regular scheme

Contents

Contents

Idea

A regular scheme (X,𝒪 X)(X,\mathcal{O}_X) is an algebraic scheme such that for every x∈Xx\in X there exists an affine open neighbourhood U⊂XU\subset X of xx such that the ring 𝒪 X(U)\mathcal{O}_X(U) is regular (many authors also require Noetherian). Equivalently, stalk 𝒪 X,x\mathcal{O}_{X,x} of the structure sheaf 𝒪 X\mathcal{O}_X at any point x∈Xx\in X (as a locally ringed space) is a regular local ring.

References

On pro-algebraic resolutions of regular schemes over algebraically complete fields:

  • Adrian Clough, Pro-algebraic resolutions of regular schemes, MSc thesis, ETC Zürich (2014) [pdf]

Last revised on June 26, 2023 at 15:57:22. See the history of this page for a list of all contributions to it.