Upper classUpper class in modern societies is the social class composed of people who hold the highest social status, usually are the wealthiest members of class society, and wield the greatest political power. According to this view, the upper class is generally distinguished by immense wealth which is passed on from generation to generation. Prior to the 20th century, the emphasis was on aristocracy, which emphasized generations of inherited noble status, not just recent wealth.
Algebraic cycleIn mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of V that is directly accessible by algebraic methods. Understanding the algebraic cycles on a variety can give profound insights into the structure of the variety. The most trivial case is codimension zero cycles, which are linear combinations of the irreducible components of the variety. The first non-trivial case is of codimension one subvarieties, called divisors.
Motive (algebraic geometry)In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically, a "motif" is the "cohomology essence" of a variety.
Projective objectIn , the notion of a projective object generalizes the notion of a projective module. Projective objects in are used in homological algebra. The dual notion of a projective object is that of an injective object. An in a category is projective if for any epimorphism and morphism , there is a morphism such that , i.e. the following diagram commutes: That is, every morphism factors through every epimorphism . If C is , i.e.
Filtration (mathematics)In mathematics, a filtration is an indexed family of subobjects of a given algebraic structure , with the index running over some totally ordered index set , subject to the condition that if in , then . If the index is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic structure gaining in complexity with time.
