symmetric monoidal (∞,1)-category of spectra
Given a commutative ring and an -algebra , this algebra is finitely generated over if it is a quotient of a polynomial ring on finitely many variables.
If moreover for a finite number of polynomials , then is called finitely presented.
A morphism of finite presentation between schemes is one which is dually locally given by finitely presented algebras.
A ring is an associative algebra over the integers, hence a -ring. Accordingly a finitely generated ring is a finitely generated -algebra, and similarly for finitely presented ring.
For rings every finitely generated ring is already also finitely presented.
Finite generation of algebras plays a role in the choice of geometry (for structured (infinity,1)-toposes) in
Last revised on April 17, 2021 at 14:34:52. See the history of this page for a list of all contributions to it.