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.
Revised on August 10, 2014 04:41:51
by Urs Schreiber