expect this “twisted” sheaf to contain grading information about N {\displaystyle N} . In particular, if N {\displaystyle N} is the sheaf associated to...

In mathematics, a twisted sheaf is a variant of a coherent sheaf. Precisely, it is specified by: an open covering in the étale topology Ui, coherent sheaves...

invertible sheaf) is O P n ( − 1 ) , {\displaystyle {\mathcal {O}}_{\mathbb {P} ^{n}}(-1),} the dual of the hyperplane bundle or Serre's twisting sheaf O P n...

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...

theorem. Picard group Divisor (algebraic geometry) Reflexive sheaf Quot scheme Twisted sheaf Essentially finite vector bundle Bundle of principal parts...

affine scheme. F(n), F(D) 1.  If X is a projective scheme with Serre's twisting sheaf O X ( 1 ) {\displaystyle {\mathcal {O}}_{X}(1)} and if F is an O X {\displaystyle...

the sheaf of relative differentials is stably isomorphic to an ( n + 1 ) {\displaystyle (n+1)} -fold sum of the dual of the Serre twisting sheaf. The...

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...

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...

sheaf on an étale site is the union of its constructible subsheaves. Twisted sheaf Milne 2012, Remark 17.6 Milne, James S. (2012). "Lectures on Étale Cohomology"...

others is developing a theory of non-abelian bundle gerbes. Twisted sheaf Azumaya algebra Twisted K-theory Algebraic stack Bundle gerbe String group Basic...

in computational complexity theory The nth tensor power of Serre's twisting sheaf O ( 1 ) {\displaystyle {\mathcal {O}}(1)} This disambiguation page lists...

{\displaystyle {\mathcal {O}}(-1)} since it corresponds to the dual of the Serre twisting sheaf O ( 1 ) {\displaystyle {\mathcal {O}}(1)} . Suppose that X {\displaystyle...

Paris Known for Giraud subcategory Giraud's axioms Gerbe Sieve Stacks Twisted sheaf Scientific career Fields Mathematics Doctoral advisor Alexander Grothendieck...

-twist of M {\displaystyle M} is a graded module defined by M ( ℓ ) n = M n + ℓ {\displaystyle M(\ell )_{n}=M_{n+\ell }} (cf. Serre's twisting sheaf in...

Serre's theorem in group cohomology Serre's theorem on affineness Serre twist sheaf Serre's vanishing theorem Serre weights Thin set in the sense of Serre...

is the n-th tensor power of the Serre twist sheaf O ( 1 ) {\displaystyle {\mathcal {O}}(1)} , the invertible sheaf or line bundle with associated Cartier...

the Serre twist sheaf O(1) on projective space, and use it to twist the structure sheaf OV any number of times, say k times, obtaining a sheaf OV(k). Then...

\mathbb {Z} }S.} If O ( 1 ) {\displaystyle {\mathcal {O}}(1)} is the twisting sheaf of Serre on P Z n {\displaystyle \mathbb {P} _{\mathbb {Z} }^{n}} ,...

polynomial equation of degree d, then its normal line bundle is the Serre twisting sheaf ⁠ O {\displaystyle {\mathcal {O}}} ⁠(d), so by the adjunction formula...

mere scheme: a sheaf in graded modules over the structure sheaf is defined in the process. The homogeneous components of this graded sheaf are denoted O...

structure sheaf (i.e., the trivial line bundle), O C P n ( 1 ) {\displaystyle {\mathcal {O}}_{\mathbb {CP} ^{n}}(1)} is Serre's twisting sheaf (i.e., the...

Origins of Twistor Theory." Jozsa, Richard (1976), "Applications of Sheaf Cohomology in Twistor Theory." Dunajski, Maciej (2009). "Twistor Theory and...

point of view exhibit some 'twisting'. Liouville's theorem (complex analysis) – Theorem in complex analysis Locally constant sheaf Hartshorne, Robin (1977)...

Extension problem Spectral sequence Abelian category Group cohomology Sheaf Sheaf cohomology Grothendieck topology Derived category Combinatorial topology...

Irrelevant ideal Locally ringed space Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem...

In mathematics, the twisted Poincaré duality is a theorem removing the restriction on Poincaré duality to oriented manifolds. The existence of a global...

complex manifolds. Alternatively, the Picard group can be defined as the sheaf cohomology group H 1 ( X , O X ∗ ) . {\displaystyle H^{1}(X,{\mathcal {O}}_{X}^{*})...

class for an element of twisted K-theory. The twisted Chern character is a differential form that represents a class in the twisted cohomology with respect...

field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of generalization of a Drinfeld module, consisting...