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algebraic irreducibility

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  • Algebraic stack — In algebraic geometry, an algebraic stack is a concept introduced to generalize algebraic varieties, schemes, and algebraic spaces. They were originally proposed in a 1969 paper[1] by Pierre Deligne and David Mumford to define the (fine) moduli… …   Wikipedia

  • Moduli of algebraic curves — In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on… …   Wikipedia

  • Hilbert's irreducibility theorem — In mathematics, Hilbert s irreducibility theorem, conceived by David Hilbert, states that an irreducible polynomial in two variables and having rational number coefficients will remain irreducible as a polynomial in one variable, when a rational… …   Wikipedia

  • Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   Wikipedia

  • Moduli space — In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as… …   Wikipedia

  • Polynomial — In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… …   Wikipedia

  • Thin set (Serre) — In mathematics, a thin set in the sense of Serre is a certain kind of subset constructed in algebraic geometry over a given field K , by allowed operations that are in a definite sense unlikely . The two fundamental ones are: solving a polynomial …   Wikipedia

  • John von Neumann — Von Neumann redirects here. For other uses, see Von Neumann (disambiguation). The native form of this personal name is Neumann János. This article uses the Western name order. John von Neumann …   Wikipedia

  • Irreducible (mathematics) — In mathematics, the term irreducible is used in several ways. * In abstract algebra, irreducible can be an abbreviation for irreducible element; for example an irreducible polynomial. * In representation theory, an irreducible representation is a …   Wikipedia

  • Perron–Frobenius theorem — In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding… …   Wikipedia

  • Inverse Galois problem — In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th centuryFact|date=February 2007, is… …   Wikipedia

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