Concept

Regular scheme

In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Every smooth scheme is regular, and every regular scheme of finite type over a perfect field is smooth. For an example of a regular scheme that is not smooth, see Geometrically regular ring#Examples.

Official source

https://en.wikipedia.org/wiki/Regular_scheme

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Related publications (3)

High Frobenius pushforwards generate the bounded derived category

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme X of prime characteristic. The main result is that when the Frobenius map on X is finite, for any compact generator G of

\mathsf {D}(X)

the Frobenius pushforward

F ^e_*G

generates the bounded derived category whenever

p^e

is larger than the codepth of X , an invariant that is a measure of the singularity of X . The conclusion holds for all positive integers e when X is locally complete intersect

Cambridge University Press (CUP)2026

Asymmetric Compute-and-Forward with CSIT

Michael Christoph Gastpar

We present a modified compute-and-forward scheme which utilizes Channel State Information at the Transmitters (CSIT) in a natural way. The modified scheme allows different users to have different coding rates, and use CSIT to achieve larger rate region. This idea is applicable to all systems which use the compute-and-forward technique and can be arbitrarily better than the regular scheme in some settings.

2014

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Jean Fasel

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d

2009

Related concepts (1)

Glossary of algebraic geometry

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. For simplicity, a reference to the base scheme is often omitted; i.e., a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism.

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