Information om | Engelska ordet ZARISKI

Exempel på hur man kan använda ZARISKI i en mening

• Thus, to prove this equality, it suffices to prove that it is verified on a non-empty open subset (for the usual topology, or, more generally, for the Zariski topology) of the space of all the coefficients.
• The generalization of the Zariski topology to the set of prime ideals of a commutative ring follows from Hilbert's Nullstellensatz, that establishes a bijective correspondence between the points of an affine variety defined over an algebraically closed field and the maximal ideals of the ring of its regular functions.
• This can also be deduced from the result stated below the third definition, and the fact that the dimension of the tangent space is equal to the Krull dimension at any non-singular point (see Zariski tangent space).
• Zariski was born Oscher (also transliterated as Ascher or Osher) Zaritsky to a Jewish family (his parents were Bezalel Zaritsky and Hanna Tennenbaum) and in 1918 studied at the University of Kyiv.
• On the other hand, the ring of germs of smooth functions at a point in an n-manifold has an n-dimensional Zariski cotangent space.
• Resolution says that such singularities can be handled rather as a (complicated) sort of compactification, ending up with a compact manifold (for the strong topology, rather than the Zariski topology, that is).
• In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.
• One expects, intuitively, that deformation theory of the first order should equate the Zariski tangent space with a moduli space.
• Nicholas Katz has applied Tannakian category techniques to show that this conjecture is essentially the same as saying that the differential Galois group G (or strictly speaking the Lie algebra g of the algebraic group G, which in this case is the Zariski closure of the monodromy group) can be determined by mod p information, for a certain wide class of differential equations.
• Consequently, to define an étale cover of a scheme X, it suffices to first cover X by open affine subschemes, that is, to take a Zariski cover, and then to define an étale cover of an affine scheme.
• The dominance ordering determines the inclusions between the Zariski closures of the conjugacy classes of nilpotent matrices.
• Rohit Parikh was married from 1968 to 1994 to Carol Parikh (née Geris), who is best known for her stories and biography of Oscar Zariski, The Unreal Life of Oscar Zariski.
• A classical result, Zariski–Nagata purity of Masayoshi Nagata and Oscar Zariski, called also purity of the branch locus, proves that on a non-singular algebraic variety a branch locus, namely the set of points at which a morphism ramifies, must be made up purely of codimension 1 subvarieties (a Weil divisor).
• Among the conjectural properties of these complexes were three properties: one connecting their Zariski cohomology to Milnor's K-theory, one connecting their etale cohomology to cohomology with coefficients in the sheaves of roots of unity and one connecting their Zariski cohomology to their etale cohomology.
• Local uniformization (proved in characteristic 0 by Zariski) can be interpreted as saying that the Zariski–Riemann space of a variety is nonsingular in some sense, so is a sort of rather weak resolution of singularities.
• The foreign mathematicians included Leonard Roth, Helmut Hasse, Wilhelm Blaschke, Paul Dubreil, Lucien Godeaux, Luitzen Brouwer, Jean Leray, Wacław Sierpiński, Wolfgang Gröbner, Heinz Hopf, Erich Kähler, Oskar Zariski, Georges De Rham, Max Deuring, Bartel Leendert Van der Waerden, Kazimierz Kuratowski, John Lighton Synge, Louis Mordell, Rolf Nevanlinna, Richard von Mises, Ernst Witt, Henri Cartan, Jacques Tits, Jean Dieudonné, Victor Kac, Francis Clarke.
• Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some other flat topologies.

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