Kähler differential

•  Algebraic geometry

  Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.

  

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•  Analytic geometry

  Analytic geometry, also known as coordinate geometry, analytical geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth.

  

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•  Homological algebra

  Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. The development of homological algebra was closely intertwined with the emergence of category theory.

  

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•  Bézout's theorem

  Bézout's theorem is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves. The theorem claims that the number of common points of two such curves X and Y is equal to the product of their degrees.

  

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•  Generalized Riemann hypothesis

  The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these L-functions, yielding various generalizations of the Riemann hypothesis.

  

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•  Calabi–Yau manifold

  In mathematics, Calabi–Yau manifolds are complex manifolds that are higher-dimensional analogues of K3 surfaces. They are sometimes defined as compact Kähler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used. They were named "Calabi–Yau spaces" by Candelas et al. (1985) after E. Calabi who first studied them, and S. T. Yau who proved the Calabi conjecture that they have Ricci flat metrics.

  

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•  Elimination theory

  In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables. The linear case would now routinely be handled by Gaussian elimination, rather than the theoretical solution provided by Cramer's rule. In the same way, computational techniques for elimination can in practice be based on Gröbner basis methods.

  

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•  Algebraic variety

  In mathematics, an algebraic variety is the set of solutions of a system of polynomial equations. Algebraic varieties are one of the central objects of study in classical (and to some extent, modern) algebraic geometry. The word "variety" is employed in the sense of a mathematical manifold, for which, in Romance languages, cognates of the word "variety" are used.

  

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•  Noncommutative geometry

  Noncommutative geometry, or NCG, is a branch of mathematics concerned with the possible spatial interpretations of algebraic structures for which the commutative law fails, that is, for which xy does not always equal yx. Although one could technically construct geometries by simply removing this condition (commutativity), the results are typically trivial or uninteresting.

  

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•  Valuation (algebra)

  In algebra, a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero in complex analysis, the degree divisibility of a number by a prime number in number theory, and the geometrical concept of contact between two algebraic or analytic varieties in algebraic geometry.

  

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• Algebraic geometry by likeorhate
• Commutative algebra by likeorhate
• Differential algebra by likeorhate

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•  Rockbox

  Rockbox is a free software replacement for the firmware held on various forms of digital audio players (DAPs). Rockbox offers an alternative to the host device's operating system firmware (in many cases without removing the original firmware) which provides a plug-in architecture for adding various enhancements and functionality to DAPs which are not present in the original OS. Enhancements include PDA functionality, applications, utilities, and games.

  

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•  Hébertists

  The Hébertists were the partisans of Jacques Hébert, the radical revolutionary journalist, in the Legislative Assembly and National Convention during the French Revolution. They were ardent supporters of the atheistic Cult of Reason, supported using force to dechristianize France, and were opposed to Robespierre's deist Cult of the Supreme Being.

  

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• 490 BC deaths by likeorhate
• Cities and towns in Croatia by likeorhate
•  Exercise Reforger

  Exercise Reforger (from return of forces to Germany) was an annual exercise conducted, during the Cold War, by NATO. The exercise was intended to ensure that NATO had the ability to quickly deploy forces to West Germany in the event of a conflict with the Warsaw Pact. The Reforger exercise itself was first conceived in 1967. The Johnson administration announced plans to withdraw approximately two divisions from Europe during 1968.

  

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