Witt group英语原文释义、词形变化、词源和词汇关系

英文释义

名词 n.

Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;

— A general method of studying the Witt group of a smooth variety is through the graded group associated to the filtration induced by the filtration of the Witt group of the function field by powers of the fundamental ideal of even rank forms.
Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms; (algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces (category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.; given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces broadly
Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms; (algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces (category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.; given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces. broadly

词形变化

Witt groups plural

词汇关系

词源

Named after German mathematician Ernst Witt (1911–1991), who introduced the concept in 1937.