• coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of...
    40 KB (6,934 words) - 00:04, 8 June 2025
  • twisting sheaf on the Proj of a ring does. Let E {\displaystyle {\mathcal {E}}} be a quasi-coherent sheaf on a scheme X {\displaystyle X} . The sheaf of symmetric...
    19 KB (3,582 words) - 05:35, 6 March 2025
  • especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties...
    26 KB (4,664 words) - 11:28, 9 October 2024
  • notion of the coherent sheaf into algebraic geometry, that is, the notion of the coherent algebraic sheaf. The notion of coherent (coherent sheaf cohomology)...
    124 KB (17,717 words) - 22:01, 1 July 2025
  • bundle p : E → Y {\displaystyle p\colon E\to Y} (or more generally a coherent sheaf on Y {\displaystyle Y} ) has a pullback to X {\displaystyle X} , f ∗...
    40 KB (6,874 words) - 12:55, 26 May 2025
  • In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module...
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  • sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...
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  • a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomology...
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  • Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian...
    69 KB (11,082 words) - 14:18, 29 June 2025
  • In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf ω X {\displaystyle \omega _{X}} together...
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  • quasi-coherent sheaf on a scheme X means an OX-module that is the sheaf associated to a module on each affine open subset of X. Finally, a coherent sheaf (on...
    44 KB (7,139 words) - 07:51, 25 June 2025
  • geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The...
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  • ν. An analytic space is coherent if its structure sheaf O {\displaystyle {\mathcal {O}}} is a coherent sheaf. A coherent sheaf of O {\displaystyle {\mathcal...
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  • y]/(xy) are Cohen–Macaulay, but is not. coherent sheaf A coherent sheaf on a Noetherian scheme X is a quasi-coherent sheaf that is finitely generated as OX-module...
    82 KB (12,496 words) - 00:02, 12 April 2025
  • module spectrum. When the structure sheaf O X {\displaystyle {\mathcal {O}}_{X}} is not coherent, working with coherent sheaves has awkwardness (namely the...
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  • geometry, a quasi-coherent sheaf on an algebraic stack X {\displaystyle {\mathfrak {X}}} is a generalization of a quasi-coherent sheaf on a scheme. The...
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  • Coherence (redirect from Coherent)
    the degree-zero subspace of a space of characters to the whole space Coherent sheaf, a specific class of sheaves having particularly manageable properties...
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  • In mathematics, the stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open...
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  • cohomology groups (for coherent sheaves) as the much finer complex topology. However, for constant sheaves such as the sheaf of integers this does not...
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  • In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space P n {\displaystyle \mathbf {P} ^{n}} is the smallest...
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  • section. A slope of a vector bundle (or, more generally, a torsion-free coherent sheaf) E with respect to H is a rational number defined as μ ( E ) := c 1...
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  • if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme Quot F ⁡ ( X ) {\displaystyle \operatorname...
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  • André–Quillen cohomology Bounded cohomology BRST cohomology Čech cohomology Coherent sheaf cohomology Crystalline cohomology Cyclic cohomology Deligne cohomology...
    44 KB (7,049 words) - 20:46, 13 January 2025
  • {\displaystyle {\mathcal {O}}_{X}} is coherent. Another important statement is as follows: for any coherent sheaf F {\displaystyle {\mathcal {F}}} on an...
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  • individual D-modules (and not more general complexes thereof); a perverse sheaf is in general represented by a complex of sheaves. The concept of perverse...
    19 KB (2,265 words) - 05:36, 25 June 2025
  • bundle gives way to that of a coherent sheaf. Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle...
    22 KB (3,604 words) - 05:48, 21 November 2024
  • is the quasi-coherent sheaf of ideals cutting out Z, then the direct image i ∗ {\displaystyle i_{*}} from the category of quasi-coherent sheaves over...
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  • Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem Grothendieck–Riemann–Roch theorem Coherent...
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  • reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The second dual of a coherent sheaf is...
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  • Stack (mathematics) (redirect from 2-sheaf)
    In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of...
    34 KB (5,116 words) - 02:17, 24 June 2025