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Topic: Structure sheaf

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coherent sheaf

sheaf theory

sheaf cohomology

invertible sheaf

James Sheafe

locally free sheaf

space associated with a sheaf

sheaf spanned by global sections

Exponential sheaf sequence

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	PlanetMath: sheaf of meromorphic functions
		As a result, the sheaf of meromorphic functions is again a constant sheaf that always yields the same value, and this value is called the function field of
		This complicated structure makes the sheaf of meromorphic functions much less useful in the differentiable category than it is for schemes or complex manifolds.
		This is version 3 of sheaf of meromorphic functions, born on 2003-08-18, modified 2004-03-28.
	planetmath.org /encyclopedia/SheafOfMeromorphicFunctions.html (299 words)

	Coherent sheaf - Wikipedia, the free encyclopedia
		In mathematics, especially in algebraic geometry and the theory of complex manifolds, a coherent sheaf F on a locally ringed space X is a sheaf isomorphic with the cokernel of a morphism of O
		For a sheaf of rings R, a sheaf F of R-modules is said to be quasi-coherent if it has a local presentation, i.e.
		The sheaf cohomology theory of coherent sheaves is called coherent cohomology.
	en.wikipedia.org /wiki/Coherent_sheaf (735 words)

	PlanetMath: structure sheaf
		with its structure sheaf corresponds to the prime spectrum of the coordinate ring
		Those who are fans of topos theory will recognize this map as an isomorphism of topos.
		This is version 1 of structure sheaf, born on 2002-05-14.
	planetmath.org /encyclopedia/StructureSheaf.html (182 words)

	Sheaf (Site not responding. Last check: 2007-10-09)
		Sheaf in sheaf this sheaf imperfect world I sheaf love sheaf sy you sheaf are indeed different.
		Context sheaf semistability and semisimplicity sheaf context sheaf goguen, sheaf meseguer eatcs monographs.
		Sheaf structure sheaf sheaf sheaf a camra member for over sheaf thirty sheaf years of customer.
	sheaf.bankdesignmagazine.com (368 words)

	[No title]
		Whenever the group is not affine, we write O for the * structure sheaf* of G. This is reconciled by the above usage since in the affine case the struc* ture sheaf* is determined by its ring of global sections.
		In the* * sheaf theo- retic approach, N is the space of global sections of a sheaf on the space of cl* osed subgroups T, the vertex V is the value of the sheaf* at the subgroup T and the fact that * *the basing map fi : N -!
		In the sheaf theoretic approach, the module T* * (H) is the cohomology of the structure sheaf with support at H. By contrast with the stand* *ard abelian category, the torsion abelian category has injective dimension 2.
	hopf.math.purdue.edu /Greenlees-Hopkins-Rosu/ellT.txt (8922 words)

	Math
		The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens to focus on what is important in mathematics.
		Structures of mathematical interest are usually characterized by some universal mapping property so the general thesis is that category theory is about determination through universals.
		This is a scan of one of Alexandre Grothendieck few publications in English, a technical report published (without copyright as an NSF report) by the Dept. of Mathematics, University of Kansas, 1958.
	www.ellerman.org /Davids-Stuff/Maths/Math.htm (2407 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-09)
		A sheaf of modules that is locally isomorphic to the direct sum of several copies of the structure sheaf.
		be the sheaf of germs of its sections.
		is the sheaf of germs of its sections (see [1], [2]); hence there is a natural one-to-one correspondence between the isomorphy classes of locally free sheaves of rank
	eom.springer.de /L/l060450.htm (184 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-09)
		» Encyclopaedia of Mathematics » I »; Invertible sheaf
		is a scheme (in particular, an algebraic variety) or an analytic space, a sheaf of
		The definition of Serre's twisted invertible sheaf is not precise enough.
	eom.springer.de /I/i052500.htm (345 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-09)
		is a sheaf of finite type, that is, it is locally generated over
		is coherent as a sheaf of modules over itself, which reduces to condition 2).
		The structure sheaf of a real-analytic space is not coherent, in general.
	eom.springer.de /c/c023020.htm (237 words)

	Ringed space - Wikipedia, the free encyclopedia
		to be the sheaf of real-valued (or complex-valued) continuous functions on open subsets of X (there may exist continuous functions over open subsets of X which are not the restriction of any continuous function over X).
		The stalk at a point x can be thought of as the set of all germs of continuous functions at x; this is a local ring with maximal ideal consisting of those germs whose value at x is 0.
		If X is a manifold with some extra structure, we can also take the sheaf of differentiable, or complex-analytic functions.
	en.wikipedia.org /wiki/Locally_ringed_space (821 words)

	[No title]
		The latter construction is a direct generalization to spectra of the Godement resolution of an abelian sheaf.
		The reason for the slogans "sheaf" and "Cech" may not be apparent, but should become clear in the next section.
		Similar arguments apply to the Bousfield-Friedlander closed model cate- gory structure on spectra, although the situation is complicated slightly by the different notion of fibration.
	www.math.purdue.edu /research/atopology/Mitchell/thomason.txt (10189 words)

	Pacific Journal of Mathematics, Volume 223, Number 2
		such that the direct image (via the first projection) of the structure sheaf of Z is locally free of rank d on T.
		Our construction proceeds by gluing together afine subschemes representing subfunctors that assign to T the subset of Z such that the direct image of the structure sheaf on T is free with a particular set of d monomials as basis.
		The coordinate rings of the subschemes representing the subfunctors are concretely described, yielding explicit local charts on the Hilbert scheme.
	pjm.math.berkeley.edu /pjm/2006/223-2/p05.xhtml (167 words)

	[No title]
		, tacitly assuming the existence of a structure sheaf
		The properties of localization show that this is a bijection; by looking at properties of containment, one also sees that it is a homeomorphism.
		Finally, the stalks of the structure sheaves on these spaces are given by the isomorphic local rings
	odin.mdacc.tmc.edu /~krc/agathos/schem2.html (1105 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		] A fiber bundle with algebraic and topological structure usually associated to a differentiable manifold M which reflects the local behavior of differentiable functions on M.
		] A local structure in which earth stresses have been relieved by many small, closely spaced fractures.
		Also known as exfoliation joint; expansion joint; pseudostratification; release joint; sheet joint; sheet structure.
	www.accessscience.com /Dictionary/S/S21/DictS21.html (2211 words)

	[No title]
		Rothstein's axiomatics is revisited and completed by a further requirement which calls for the completeness of the rings of sections of the structure sheaves, and allows one to dispose of some undesirable features of Rothstein supermanifolds.
		The {\sl sheaf $\sh {D}er\A$ of derivations} of $\A$ is by definition the completion of the presheaf of $\A$-modules $U\mapsto \bigl\lbrace\text{graded derivations of}\ \A_{\vert U}\bigr\rbrace$, where a graded derivation of $\A_{\vert U}$ is an endomorphism of sheaves of graded $B$-algebras $D\colon \A_{\vert U}\to \A_{\vert U}$ which fulfills the graded Leibniz rule, sc\.
		This means that $\rest{\Q},W$ is isomorphic with its associated sheaf $\rest{\bar\A},W$ for each coordinate neighbourhood $W$, so that $\bar \A$ can be endowed with a structure of a sheaf of {\sl complete\/} Hausdorff locally convex graded $B$-algebras.
	www.ma.utexas.edu /mp_arc/papers/92-182 (3800 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-09)
		is a sheaf of associative and commutative rings with a unit element.
		, while the morphisms are compatible with the structure of the algebras.
		is the sheaf of germs of continuous functions on
	eom.springer.de /r/r082460.htm (196 words)

	Huybrechts on Branes in K3, I \| The String Coffee Table
		with a vector bundle on it) is encoded in a coherent sheaf on
		The general brane for the B-model string is obtained by stacking a collection of geometric branes and anti-branes on top of each other and turning on tachyon condensates between them (which in part mutually annihilates them, the remaining piece being a general brane).
		trivial this is the “ideal sheaf” (with “ideal” in the sense of ideal of a ring)
	golem.ph.utexas.edu /string/archives/000796.html (1294 words)

	Algebraic variety - Wikipedia, the free encyclopedia
		A scheme is a locally ringed space such that every point has a neighbourhood, which, as a locally ringed space, is isomorphic to a spectrum of a ring.
		Basically, a variety is a scheme whose structure sheaf is a sheaf of K-algebras with the property that the rings R that occur above are all domains and are all finitely generated K-algebras, i.e., quotients of polynomial algebras by prime ideals.
		These varieties have been called 'varieties in the sense of Serre', since Serre's foundational paper FAC on sheaf cohomology was written for them.
	en.wikipedia.org /wiki/Algebraic_variety (1111 words)

	Siu (Site not responding. Last check: 2007-10-09)
		A multiplier is a function such that local a priori estimates for partial differential equations hold only after the test function is multiplied by it.
		The ideal sheaf consisting of multipliers identifies the location and the jet orders where local a priori estimates fail to hold.
		Solvability of a partial differential equation is reduced to algebraic conditions which force the multiplier ideal sheaf to be the structure sheaf.
	www.math.miami.edu /anno/winter05/siu.htm (173 words)

	[No title]
		Crossley and Sarah Whitehouse Abstract Text: The dual Steenrod algebra can be expressed as the homotopy of a smash product of two copies of the Eilenberg-MacLane spectrum, and the conjugation arises by permutation of the two factors.
		We show that for a certain class of Hopf algebras the cohomology ring is independent of the coproduct provided $n$ and $(n-2)!$ are invertible in the ground ring.
		The obstraction to its existence turns out to admit a very simple expression in terms of characteristic classes of $X$, namely it is expressed in terms of the second component of Chern character of the tangent bundle of $X$.
	www.lehigh.edu /~dmd1/h831 (1053 words)

	[No title]
		This model structure is related to the strict structure of Edwards and Hastings.
		Toric manifolds have such structure, and the purpose of this note is to raise some natural questions about the symplectic cobordism classes of such manifolds.
		Five examples are sketched, four corresponding to d=1 and one to d=3, and the paper concludes with a remark about adjoint structures on such categories.
	www.lehigh.edu /dmd1/public/www-data/h716 (1416 words)

	Vector bundle - Wikipedia, the free encyclopedia
		Complex vector bundles are important in many cases, too; they are a special case, meaning that they can be seen as extra structure on an underlying real bundle.
		The collection of these vector spaces is a sheaf of vector spaces on X.
		This is a special case of reduction of the structure group of a bundle.
	en.wikipedia.org /wiki/Vector_bundle (1150 words)

	34a (Site not responding. Last check: 2007-10-09)
		This should play the role of the structure sheaf.
		This carries a complex structure which interchanges horizontal and vertical directions in the tangent bundle.
		Remark: There was some discussion of phases for complex patching during the conference.
	www.aimath.org /WWN/amoebas/articles/html/34a (594 words)

	Seminars (Site not responding. Last check: 2007-10-09)
		the generalized sheaf of differential operators D_X(L) where L is a
		a'th sheaf of jets of the linebundle L is a sheaf of bimodules on X
		right module over the structure sheaf on the projective line, projective
	www.math.ntnu.no /seminars/?kategori=Algebraseminar (1012 words)

	Finiteness of de Rham cohomology in rigid analysis, Elmar Grosse-Klönne
		For a large class of smooth dagger spaces–rigid spaces with overconvergent structure sheaf–we prove finite dimensionality of de Rham cohomology.
		[11]E. Grosse-Klönne, Rigid analytic spaces with overconvergent structure sheaf, J. Reine Angew.
		[20] K. Kato, ``Logarithmic structures of Fontaine-Illusie'' in Algebraic Analysis, Geometry, and Number Theory, Johns Hopkins Univ. Press, Baltimore, 1989, 191--224.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1087575225 (494 words)

	4a (Site not responding. Last check: 2007-10-09)
		is a Calabi-Yau variety if it has trivial canonical sheaf (i.e., the canonical sheaf is isomorphic to the structure sheaf).
		Del Pezzo surface : A Del Pezzo surface is a Fano variety of dimension two.
		of elliptic curves with extra structure and Shimura curves which parametrize quaternionic multiplication abelian surfaces with extra structure.
	www.aimath.org /WWN/qptsurface2/articles/html/4a (1057 words)

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