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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
Twisted_sheaf
Projective analogue of the spectrum of a ring
expect this “twisted” sheaf to contain grading information about N {\displaystyle N} . In particular, if N {\displaystyle N} is the sheaf associated to
Proj_construction
Vector bundle existing over a Grassmannian
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
Tautological_bundle
Short exact sequence of sheaves on projective space
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
Euler_sequence
Generalization of vector bundles
theorem. Picard group Divisor (algebraic geometry) Reflexive sheaf Quot scheme Twisted sheaf Essentially finite vector bundle Bundle of principal parts
Coherent_sheaf
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
Reflexive_sheaf
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"
Torsion_sheaf
Sheaf consisting of modules on a ringed space; generalizing vector bundles
In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf of abelian groups F such that, for any open subset U of
Sheaf_of_modules
Tool to track locally defined data attached to the open sets of a topological space
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
Sheaf_(mathematics)
Topics referred to by the same term
in computational complexity theory The nth tensor power of Serre's twisting sheaf O ( 1 ) {\displaystyle {\mathcal {O}}(1)} This disambiguation page lists
O(n)
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
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
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
List of things named after Jean-Pierre Serre
List_of_things_named_after_Jean-Pierre_Serre
Construct in mathematics
others is developing a theory of non-abelian bundle gerbes. Twisted sheaf Azumaya algebra Twisted K-theory Algebraic stack Bundle gerbe String group Basic
Gerbe
Locally constant sheaf of abelian groups on topological space
between cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from point to point. Local coefficient
Local_system
Number of "holes" of a surface
\Gamma (\mathbb {P} ^{2},{\mathcal {O}}_{\mathbb {P} ^{2}}(d))} of the twisting sheaf has geometric genus g = ( d − 1 ) ( d − 2 ) 2 − s , {\displaystyle g={\frac
Genus_(mathematics)
Property of algebraic varieties and complex manifolds
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
Geometric_genus
depending on trim, but Sheaffer also offers 14K Gold nibs in certain countries in Asia. The Ballpoint is a twist-action. Sheaffer Prelude pens come in a
Sheaffer_Prelude
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
Homogeneous_coordinate_ring
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
Algebraic geometry of projective spaces
Algebraic_geometry_of_projective_spaces
French mathematician (1936–2007)
Paris Known for Giraud subcategory Giraud's axioms Gerbe Sieve Stacks Twisted sheaf Scientific career Fields Mathematics Doctoral advisor Alexander Grothendieck
Jean_Giraud_(mathematician)
Algebraic variety in a projective space
\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}} ,
Projective_variety
Algebraic structure used in topology
Alexander–Spanier cohomology or sheaf cohomology). (Here sheaf cohomology is considered only with coefficients in a constant sheaf.) These theories give different
Cohomology
Ruled surface over the projective line
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
Hirzebruch_surface
Type of algebraic structure
-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
Graded_ring
Vector bundle of rank 1
{\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
Line_bundle
Characteristic classes of vector bundles
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
Chern_class
massless field equations, to sheaf cohomology groups on complex projective space. The projective space in question is the twistor space, a geometrical space
Penrose_transform
Extends Poincaré duality beyond oriented manifolds
In mathematics, the twisted Poincaré duality is a theorem removing the restriction on Poincaré duality to oriented manifolds. The existence of a global
Twisted_Poincaré_duality
Theory proposed by Roger Penrose
Origins of Twistor Theory." Jozsa, Richard (1976), "Applications of Sheaf Cohomology in Twistor Theory." Dunajski, Maciej (2009). "Twistor Theory and
Twistor_theory
Type of mathematical function
point of view exhibit some 'twisting'. Liouville's theorem (complex analysis) – Theorem in complex analysis Locally constant sheaf Hartshorne, Robin (1977)
Locally_constant_function
Irrelevant ideal Locally ringed space Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem
List of algebraic geometry topics
List_of_algebraic_geometry_topics
locally constant sheaf. Orientation character, a characteristic form related to the orientation line bundle, useful to formulate Twisted Poincaré duality
Flat_vector_bundle
Generalisations of Serre duality in mathematics
classical algebraic geometry. This was re-expressed, with the advent of sheaf theory, in a way that made an analogy with Poincaré duality more apparent
Coherent_duality
2010 Canadian TV series or program
Retrieved 17 December 2016. 2011 nominees (PDF) Golden Sheaf Awards 2012 nominees (PDF) Golden Sheaf Awards "2011 nominess" (PDF). leoawards.com. Retrieved
Todd and the Book of Pure Evil
Todd_and_the_Book_of_Pure_Evil
Concept in mathematics
field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of generalization of a Drinfeld module, consisting
Drinfeld_module
Mathematical group occurring in algebraic geometry and the theory of complex manifolds
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}^{*})
Picard_group
In mathematics, more specifically sheaf theory, a branch of topology and algebraic geometry, the exceptional inverse image functor is the fourth and most
Exceptional inverse image functor
Exceptional_inverse_image_functor
the sheaf of rings on G/B formed by taking the *-pushforward of DG/U along the T-bundle G/U → G/B, a sheaf of rings whose center is the constant sheaf of
Beilinson–Bernstein localization
Beilinson–Bernstein_localization
theory Ring theory Scheme theory Semigroup theory Set theory Shape theory Sheaf theory Sieve theory Singularity theory Soliton theory Spectral theory String
List_of_mathematical_theories
Branch of mathematics studying functions of a complex variable
variables makes use of additional techniques such as Banach algebras and sheaf theory. It is often concerned with questions of interest in algebraic geometry
Complex_analysis
Right inverse of a fiber bundle map
"twisted". More precisely, obstructions "obstruct" the possibility of extending a local section to a global section due to the space's "twistedness".
Section_(fiber_bundle)
Concept in algebraic geometry
(2005). Given a function (more generally, a section of a quasicoherent sheaf) defined on an open subset of an algebraic variety (or scheme), local cohomology
Local_cohomology
Suburb of Greater London, England
2022. Sheaf 2015, pp. 80–86, 100–108. Sheaf & Howe 1995, pp. 91–93. Heath 2000, pp. 9–10. Orton 1965, pp. 48–49, 63. Sheaf 1997, pp. 12–13. Sheaf 2015
Hampton,_London
women in the Italian states. Many women twisted their long hair with cords or ribbons and wrapped the twists around their heads, often without any cap
1300–1400_in_European_fashion
American writer (1920–1994)
Infobase Learning. p. 11. ISBN 9781438148373. Retrieved July 15, 2025. "Sheaf, Hearse, Coffin, Poetry NOW" by E.V. Griffith (Hearse Press, 1996), pp.
Charles_Bukowski
Algebraic topology uses abstract algebra to study topological spaces
Extension problem Spectral sequence Abelian category Group cohomology Sheaf Sheaf cohomology Grothendieck topology Derived category Combinatorial topology
List of algebraic topology topics
List_of_algebraic_topology_topics
Geometry of Deligne cohomology Notes on differential cohomology and gerbes Twisted smooth Deligne cohomology Bloch's Conjecture, Deligne Cohomology and Higher
Deligne_cohomology
Supergeometric generalization of a manifold
formulation, a smooth supermanifold is a locally ringed space whose structure sheaf is locally isomorphic to the tensor product of the ring of ordinary smooth
Supermanifold
Concept in ring theory
on ( X , O X ) {\displaystyle (X,{\mathcal {O}}_{X})} into a 'twisted-form' of the sheaf M n ( O X ) {\displaystyle M_{n}({\mathcal {O}}_{X})} . Milne
Azumaya_algebra
the notion of smoothness from calculus. Instead it is built using sheaf theory and sheaf cohomology. Abstract harmonic analysis A modern branch of harmonic
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
strip of a corn field left fallow. The fear of being left with the last sheaf of the harvest called the cailleach (kulyach etc.) or gobhar bhacach (the
Bauk_(field)
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
Bundle_gerbe
Application of homotopy to algebraic varieties
A simplicial sheaf X {\displaystyle {\mathcal {X}}} is called A 1 {\displaystyle \mathbb {A} ^{1}} -local if for any simplicial sheaf Y {\displaystyle
A¹_homotopy_theory
Fiber bundle whose fibers are projective spaces
) {\displaystyle \mathbb {P} (E)} for some vector bundle (locally free sheaf) E. Every vector bundle over a variety X gives a projective bundle by taking
Projective_bundle
Group of four demons in Hindu mythology
"the one with the tusk," who is said to possess a twisted trunk (vakratuṇḍa) and who holds a corn-sheaf, a sugar cane, and a club. This description of Dantin
Vinayakas
Mathematical object studied in the field of algebraic geometry
of a ring. Basically, a variety over k is a scheme whose structure sheaf is a sheaf of k-algebras with the property that the rings R that occur above are
Algebraic_variety
Formalism in homological algebra
Lf^{*}} is isomorphic to f!(−d)[−2d], where (−d) denotes the dth inverse Tate twist and [−2d] denotes a shift in degree by −2d. Furthermore, suppose that f
Six_operations
U.S. state flag
shield of horizontal orange, blue, and white stripes. On the stripes are a sheaf of wheat, an ear of corn, and an ox standing on grass, all representing
Flag_of_Delaware
Writing implement with nib and internal ink reservoir
followed by A. A. Waterman's twist-filler. The tipping point, however, was the runaway success of Walter A. Sheaffer's lever-filler, introduced in 1912
Fountain_pen
Continuous surjection satisfying a local triviality condition
Klein bottle, which can be viewed as a "twisted" circle bundle over another circle. The corresponding non-twisted (trivial) bundle is the 2-torus, S 1 ×
Fiber_bundle
Correspondsnce between Higgs bundles and fundamental group representations
{\mathcal {F}})/B^{k}(X,{\mathcal {F}})} of sheaf cocycles by sheaf coboundaries is always well-defined. When the sheaf F {\displaystyle {\mathcal {F}}} is not
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Panlo is the District 9 male tribute in the 10th Hunger Games. He and Sheaf die from injuries sustained in the bombing attack. In the movie, he was
List of The Hunger Games characters
List_of_The_Hunger_Games_characters
Concept in differential geometry
glueing properties (analogously to the glueing properties satisfied by a sheaf). In order to state such properties precisely, one needs to define (pre)stacks
Differentiable_stack
Affine space over the complex numbers
holomorphic functions on a complex affine space A forms a sheaf of rings on it. By definition, such a sheaf associates to each (analytic) open subset U of A the
Complex_affine_space
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
Quot_scheme
geometry) Duality theory for distributive lattices Dualizing complex Dualizing sheaf Eckmann–Hilton duality Esakia duality Fenchel's duality theorem Grothendieck
List_of_dualities
English actor and screenwriter
has appeared in the films Plenty, Notting Hill, Roman Polanski's Oliver Twist, 44 Inch Chest, The Confessions and Rogue One: A Star Wars Story, and on
Andy_de_la_Tour
Generalizes the Kodaira vanishing theorem
^{p}(F))} equal zero. Here, Ω p ( F ) {\textstyle \Omega ^{p}(F)} denotes the sheaf of holomorphic (p,0)-forms taking values on F. The theorem states that,
Nakano_vanishing_theorem
Japanese manga series
gunfighting skills are undeniable, but he lacks social polish. Agera Dutch Sheaffer An observant young woman who becomes Jimmu's first follower. Mira Abigail
The_Marshal_King
and H is a hyperplane section, then a vector bundle (or a torsion-free sheaf) W is called stable (or sometimes Gieseker stable) if χ ( V ( n H ) ) rank
Stable_vector_bundle
Device dispensing ink over a metal ball at its point
Ohto Paper Mate Parker Pelikan Pierre Cardin Pilot Reynolds Sailor Sakura Sheaffer Stabilo Scripto Staedtler Tombow TOZ Penkala Uni-ball Yard-O-Led Zebra
Ballpoint_pen
English actor and filmmaker (1889–1977)
Friedrich, p. 393. Louvish, p. 135. Chaplin, pp. 423–444; Robinson, p. 670. Sheaffer, pp. 623, 658. Chaplin, pp. 423, 477. Robinson, p. 519. Robinson, pp. 671–675
Charlie_Chaplin
American actress (born 1941)
Northwestern University for a brief time; In a September 1959 advertisement for Sheaffer pens, she appears as "Ann Margret Olson, freshman, Northwestern University
Ann-Margret
Mathematical parametrization of vector spaces by another space
OX denotes the structure sheaf of continuous real-valued functions on X, then F becomes a sheaf of OX-modules. Not every sheaf of OX-modules arises in
Vector_bundle
Canadian brewer
the red maple leaf on the logo has also been changed to a stylized red sheaf of wheat, which Labatt calls its symbol of "brewing quality." Under the
Labatt_Brewing_Company
Construct in algebraic geometry
mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such
Cotangent_complex
Hindu god of new beginnings, wisdom and luck
identification. The description of Dantin, possessing a twisted trunk (vakratuṇḍa) and holding a corn-sheaf, a sugar cane, and a club, is so characteristic of
Ganesha
1991 Canadian film by Manon Briand
Luce-Guilbault for Most Promising Young Actor. In 1992 the film won Canada's Golden Sheaf Awards for Best Drama Over 30 Minutes and Best Director at the Yorkton Film
Letters_of_Transit_(film)
Eleventh series of The Great British Bake Off
decorative bread plaque in the style of a traditional harvest festival sheaf, portraying the one thing in life they are most grateful for, in 3 hours
The Great British Bake Off series 11
The_Great_British_Bake_Off_series_11
American reality television series
Kim, Shavi Lewis, Geoffrey Mac, Delvin McCray, Tyler Neasloney, Veronica Sheaffer, Melanie Trygg and Nancy Volpe-Beringer. At age 64, Nancy Volpe-Beringer
Project_Runway
Mathematical conjecture
of X ^ {\displaystyle {\hat {X}}} , the simplest example of a coherent sheaf appearing in the derived category of the mirror manifold. If the mirror
SYZ_conjecture
Writing pen manufacturer
from the original on March 9, 2014. "Parker An Invitation to Fly". ParkerSheaffer.com. May 23, 2020. Archived from the original on July 29, 2020. Retrieved
Parker_Pen_Company
Brand of luxury writing instruments
fountain, ballpoint pens, and rollerball pens. The classic line features 0.7mm twist action mechanical pencils with barrels encased in precious woods such as
Graf_von_Faber-Castell
British actor (1927–2015)
According to one reviewer, his performance in Anglo Saxon earned him "a sheaf of golden notices and put him at the top of the ratings for mature heart-throbs
Richard_Johnson_(actor)
British-Lebanese mathematician (1929–2019)
paper: a short note on twisted cubics. He started research under W. V. D. Hodge and won the Smith's prize for 1954 for a sheaf-theoretic approach to ruled
Michael_Atiyah
Pseudoscientific claims of past alien contact
Charlatanism?" Archived August 24, 2019, at the Wayback Machine; Robert Sheaffer. Via Debunker.com; originally published in NICAP UFO Investigator, October/November
Ancient_astronauts
Generalized manifold
degrees of freedom are the twisted states, which are strings "stuck" at the fixed points. When the fields related with these twisted states acquire a non-zero
Orbifold
Fictional character, associate and friend of Sherlock Holmes
to follow his deductions, and to observe the untidiness of attire, the sheaf of legal papers, the watch-charm, and the breathing which had prompted them
Dr._Watson
Season of television series
Sergio Guadarrama - SG Shavi Lewis - SL Tyler Neasloney - TN Veronica Sheaffer - VS Victoria Cocieru - VC Original airdate: December 5, 2019 With luggage
Project_Runway_season_18
Riemannian manifold with SU(n) holonomy
Tot ( ω S ) {\displaystyle {\text{Tot}}(\omega _{S})} of the canonical sheaf ω S {\displaystyle \omega _{S}} for an algebraic surface S {\displaystyle
Calabi–Yau_manifold
Manufacturer of pens and pencils
configurations. The Dialog is a cap-less fountain pen with twist action to expose the 14 carat gold nib. Twisting also causes the pen's clip to retract into the barrel
Lamy
History of an emblematic system
seals of this type, belonging to Hugh III, Count of Saint-Pol, bearing a sheaf of oats in the field and dating from 1127/1129, Hugh I of Rodez (an eagle
Origin_of_coats_of_arms
Ancient technique for reproducing images or text
Retrieved 2015-10-18. Forrer, Matthi, Willem R. van Gulik, Jack Hillier A Sheaf of Japanese Papers, The Hague, Society for Japanese Arts and Crafts, 1979
Woodblock_printing_in_Japan
Irish holiday and Gaelic harvest festival
the summit as a sign that summer was ending. In other places, the first sheaf of the harvest was buried. There were also faction fights, whereby two groups
Lughnasadh
Christian religious group in England from 1846 to 1956
William Blake's Jerusalem depicting, as they do, a fiery chariot and a sheaf of arrows (presumably of desire), while the main steeple is clearly surmounted
Agapemonites
Generalization of matrix trace
endomorphisms of locally free sheaves of finite rank on a ringed space, see Sheaf of modules § Operations. If C is the ∞-category of chain complexes of modules
Categorical_trace
Japanese stationery company
Sharp Kerry, Sharp P200 series, Multi 8 (All-purpose mechanical pencil), Twist-Erase, Q-Erase, Quicker Clicker, Graph 1000, Graphgear (500, 800 and 1000)
Pentel
Topological space that locally resembles Euclidean space
fixed dimension. Sheaf-theoretically, a manifold is a locally ringed space, whose structure sheaf is locally isomorphic to the sheaf of continuous (or
Manifold
Branch of mathematics
the Adams operations. In high energy physics, K-theory and in particular twisted K-theory have appeared in Type II string theory where it has been conjectured
K-theory
Specific algebraic group
GL_{n}(\mathbb {Z} ))} , where the coefficient group forms a constant sheaf. In particular, twisted forms of a split torus T over a field K are parametrized by
Algebraic_torus
travel, tourism, insurance
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
TWISTED SHEAF
travel, tourism, insurance