This entry is about the notion of a residue field in algebraic geometry. There is another (related) notion of a residue field in constructive mathematics; see weak Heyting field.
symmetric monoidal (∞,1)-category of spectra
Given a local ring , by the definition there is a maximal ideal . The quotient is therefore a division ring, and in commutative case, therefore a field, called the residue field. In algebraic geometry, the residue field at a point of a scheme is the residue field of the corresponding stalk of the structure sheaf, which is by the definition a local ring.
Last revised on January 28, 2024 at 05:14:36. See the history of this page for a list of all contributions to it.