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Serre–Tate Theorem
In algebraic geometry, the Serre–Tate theorem says that an abelian scheme and its p-divisible group have the same infinitesimal Deformation Theory, deformation theory. This was first proved by Jean-Pierre Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then John Tate (mathematician), John Tate gave a proof in the general case by a different method. Their proofs were not published, but they were summarized in the notes of the Lubin–Serre–Tate seminar (Woods Hole, 1964). Other proofs were published by William Messing, Messing (1962) and Vladimir Drinfeld, Drinfeld (1976). References * : see, vol.2, p. 854, comments on Tate's letter from Jan.10, 1964. * Abelian varieties Theorems in algebraic geometry {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |