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In mathematics, local class field theory, introduced by Helmut Hasse, [1] is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite residue field: hence every local field is isomorphic (as a topological field) to the real numbers R, the complex numbers C, a finite extension of ...
Grade 9 subjects include Danish, English, Christian studies, history, social studies, mathematics, geography, biology, physics/chemistry and German and French as electives. [11] Students must sit compulsory school-leaving exams at the end of grade 9, and must also complete a mandatory project assignment during the year. [11]
Ngô Bảo Châu (Vietnamese: [ŋo ɓa᷉ːw cəw], born June 28, 1972) [3] is a Vietnamese-French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad).
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
In 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 origins of class field theory lie in the quadratic reciprocity law proved by Gauss. The generalization took place as a long-term historical project, involving quadratic forms and their 'genus theory', work of Ernst Kummer and Leopold Kronecker/Kurt Hensel on ideals and completions, the theory of cyclotomic and Kummer extensions.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The set of arithmetic functions forms a commutative ring, the Dirichlet ring, under pointwise addition, where f + g is defined by (f + g)(n) = f(n) + g(n), and Dirichlet convolution.