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Topic: Serre duality

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	Kids.Net.Au - Encyclopedia > Jean-Pierre Serre
		Jean-Pierre Serre (born September 15, 1926) was educated at the Lycée de Nimes[?] and then the Ecole Normale Supérieure[?] in Paris from 1945 to 1948.
		Serre was awarded his doctorate from the Sorbonne in 1951.
		Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003 for his contributions to topology, algebraic geometry and number theory.
	www.kids.net.au /encyclopedia-wiki/je/Jean-Pierre_Serre (116 words)

	Jean-Pierre Serre (Site not responding. Last check: 2007-09-03)
		Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology.
		While Serre subsequently moved field - at this point he apparently thought that homotopy theory where he had started was already over-technical - Weyl's perception that the central place of classical analysis had been challenged by abstract algebra has subsequently been justified, as has his assessment of Serre's place in this change.
		Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003.
	www.1-free-software.com /en/wikipedia/j/je/jean_pierre_serre.html (431 words)

	Jean-Pierre Serre - Wikipedia, the free encyclopedia
		Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the Ecole Normale Supérieure in Paris.
		Serre's thesis refers to his dissertation on the Leray-Serre spectral sequence associated to a fibration.
		Amongst Serre's early candidate theories (1954/55) was one based on Witt vector coefficients.
	en.wikipedia.org /wiki/Jean-Pierre_Serre (552 words)

	Riemann-Roch theorem
		An n-dimensional generalisation was found and proved by Hirzebruch, as an application of characteristic classes[?] in algebraic topology.
		At about the same time Jean-Pierre Serre was giving the general form of Serre duality[?], as we now know it.
		Alexander Grothendieck gave a general and influential proof of the Riemann-Roch theorem in algebraic geometry.
	www.ebroadcast.com.au /lookup/encyclopedia/ri/Riemann-Roch_theorem.html (646 words)

	Duality (mathematics) - Wikipedia, the free encyclopedia
		In another group of dualities, the objects of one theory are translated into objects of another theory and the morphisms between objects in the first theory are translated into morphisms in the second theory, but with direction reversed.
		Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed.
		Dual graph is a concept in graph theory.
	en.wikipedia.org /wiki/duality_(mathematics) (314 words)

	Serre duality - Wikipedia, the free encyclopedia
		In algebraic geometry, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality) for vector bundles and the more general coherent sheaves.
		Serre duality of curves is therefore something very classical; but it has interesting light to cast.
		While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot just be a single sheaf in the absence of some hypothesis of non-singularity on V.
	en.wikipedia.org /wiki/Serre_duality (413 words)

	NationMaster - Encyclopedia: Derived category
		Coherent duality in mathematics refers to a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the local theory.
		In coherent sheaf theory, pushing to the limit of what could be done with Serre duality without the assumption of a non-singular scheme, the need to take a whole complex of sheaves became apparent.
		In fact the Cohen-Macaulay ring condition, a weakening of non-singularity, corresponds to the existence of a single dualizing sheaf; and this is far from the general case.
	www.nationmaster.com /encyclopedia/Derived-category (1325 words)

	Serre duality - Definition, explanation
		In algebraic geometry, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality) for vector bundles and the more general coherent sheaves.
		Serre duality of curves is therefore something very classical; but it has interesting light to cast.
		While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot just be a single sheaf in the absence of some hypothesis of non-singularity on V.
	www.calsky.com /lexikon/en/txt/s/se/serre_duality.php (420 words)

	PlanetMath: Serre duality
		While Serre duality is not in a strict sense a generalization of Poincaré duality, they are philosophically similar, and both fit into a larger pattern on duality results.
		Cross-references: duality, similar, Poincaré duality, strict, locally free, nonsingular, isomorphism, sheaf, coherent sheaf, field, algebraically closed, projective varieties, dimension, schemes
		This is version 9 of Serre duality, born on 2003-08-15, modified 2007-01-14.
	www.planetmath.org /encyclopedia/DualizingSheaf.html (145 words)

	Serre Duality (Site not responding. Last check: 2007-09-03)
		On Generalizing a Theorem of Serre: A Case Study in the Duality Between Algebra...
		Serre duality on complex supermanifolds, Carl Haske, R. Wells, Jr....
		N = 1 dualities and the dynamics of brane...
	www.scienceoxygen.com /math/735.html (133 words)

	Duality (mathematics) - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-09-03)
		For the general notion in category theory that underlies these dualities, see duality (category theory) and dual (category theory).
		dual numbers, a certain associative algebra; the term "dual" here is unrelated to the notions given above.
		Duality in Analytic Number Theory (Cambridge Tracts in Mathematics)
	encyclopedia.worldsearch.com /duality_(mathematics).htm (323 words)

	Serre duality (Site not responding. Last check: 2007-09-03)
		In algebraic geometry Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality) - for vector bundles and the more general coherent sheaves.
		Serre duality of curves is therefore something classical; but it has interesting light to For example in Riemann surface theory the deformation theory of complex is studied classically by means of quadratic (namely sections of L(K
		In the generalisation of Alexandre Grothendieck Serre duality becomes a part of duality in a much broader setting.
	www.freeglossary.com /Serre_duality (528 words)

	Math JS Milne Preprints
		For an abelian variety A and its dual B over a local field of prime characteristic, prove that A(K) is dual to the Weil-Chatelet group of B.
		Gives a short proof of the theorem, which is a duality for the cohomology groups of finite flat group schemes over complete discrete valuation rings.
		Includes proofs of all the main duality theorems in algebraic number theory and arithmetic geometry, some of which were previously unavailable.
	www.jmilne.org /math/Preprints (2580 words)

	[No title]
		GROSS-HOPKINS DUALITY N. In [8] Hopkins and Gross state a theorem revealing a profound relationship be* tween two different kinds of duality* in stable homotopy theory.
		Then for any coherent sheaf F on S we have a Serre duality isomorphism Hk(S; Hom(F; d)) = Hom (Hd-k(S; F); C): This can be seen as a special case of the Grothendieck duality theorem for a pr* *oper morphism [7], which is formulated in terms of functors between derived categories.
		The Hopkins-Gross theorem is a ki* nd of analog of Serre* duality in the K(n)-local stable homotopy category.
	hopf.math.purdue.edu /Strickland/st-ghd.txt (4246 words)

	PlanetMath: Serre duality
		While Serre duality is not in a strict sense a generalization of Poincaré duality, they are philosophically similar, and both fit into a larger pattern on duality results.
		Cross-references: Poincaré duality, strict, pairing, locally free, nonsingular, sheaf, coherent sheaf, perfect, field, algebraically closed, projective varieties, dimension, schemes, states
		This is version 5 of Serre duality, born on 2003-08-15, modified 2005-03-10.
	planetmath.org /encyclopedia/DualizingSheaf.html (134 words)

	php-deluxe.net - description: Coherent-duality
		'''Coherent duality''' in mathematics refers to a number of generalisations of Serre+duality, applying to coherent+sheaves, in algebraic+geometry and complex+manifold theory, as well as some aspects of commutative+algebra that are part of the 'local' theory.
		Then according to a general principle, Grothendieck%27s+relative+point+of+view, the theory of Jean-Pierre+Serre was extended to a proper+morphism; Serre duality was recovered as the case of the morphism of a non-singular projective+variety (or complete+variety) to a point.
		While Serre duality uses a line+bundle or invertible+sheaf as a '''dualizing sheaf''', the general theory (it turns out) cannot be quite so simple.
	www.php-deluxe.net /wiwimod,index.page,Coherent-duality.htm (492 words)

	Serre duality (Site not responding. Last check: 2007-09-03)
		In fact the basic relation of thetheorem involved L(D) and L(K-D), where D is a divisor and K a divisor of the canonical class.
		In the generalisation of Alexandre Grothendieck, Serre duality becomes a part of coherent duality in a muchbroader setting.
		The statement ofthe theorem is recognisably Serre's, however.
	www.therfcc.org /serre-duality-206634.html (327 words)

	Coherent sheaf - Term Explanation on IndexSuche.Com
		In the basic work of Serre, it was shown first that compact complex manifolds have the property that their sheaf_cohomology for any coherent sheaf consists of vector spaces of finite dimension.
		The Serre result is the case of a morphism to a point (which is therefore already a deep result).
		The duality theory in scheme_theory that extends Serre_duality is called coherent_duality (sometimes ''Grothendieck duality'').
	www.indexsuche.com /Coherent_sheaf.html (453 words)

	iqexpand.com (Site not responding. Last check: 2007-09-03)
		Trust In Years Of Experience Serre Financial is a successful group plans consulting firm with 50 years of extensive tax knowledge at our disposal and...
		Serre Chevalier is sponsored by: Serre Chevalier Resort Information Trails (Pistes): 110 Halfpipes: 2 Serre Chevalier Webcam Serre Chevalier Piste Map Visitor's Photographs of Serre Chevalier Summit:...
		Serre Chevalier is in The Southern French Alps.
	serre.iqexpand.com (651 words)

	Georges Serré
		In his studio in Sevres he produced a high quality, refined and very personal pottery, sometimes flawed and thus full of charm.
		In his work one finds the duality between a close-to-earth, matter-sensitive human being and the strictness and perfection of the way of teaching in Sevres in 1902.
		His work is characterized by two main trends : the pieces inspired by Emile Decoeur’s pottery and those in baked clay.
	www.ceramique1900.com /serre.html (95 words)

	ALGA 02 - Abstracts (Site not responding. Last check: 2007-09-03)
		If one (or equivalently both) of the linked schemes is Cohen-Macaulay, Serre duality shows that the cohomology of the canonical module is expressible in terms of the cohomology of the scheme itself.
		We here investigate the case where both schemes are not Cohen-Macaulay, and describe the behaviour of deficiency modules (the graded duals of cohomology modules) under liaison in the case of surfaces and three-folds.
		This study relies on an extension of Serre duality to non Cohen-Macaulay coherent sheaves.
	w3.impa.br /~alga/alga02/abstracts/abstracts.html (333 words)

	On Generalizing a Theorem of Serre: A Case Study in the Duality Between Algebra and Topology (Site not responding. Last check: 2007-09-03)
		In tandem with his computation of the cohomology of Eilenberg-MacLane spaces, J.P. Serre demonstrated that a simply connected space with finite mod 2 cohomology and with finitely many 2-components in its homotopy is, in modern parlance,
		Recently, it was shown that Serre's methods could be dualized to demonstrate that his theorem holds for simply connected simplicial commutative algebras over a field of characteristic 2, with homotopy in place of cohomology and André-Quillen homology in place of the 2-components of homotopy.
		In recent work aimed at generalizing Quillen's conjecture, a generalization of the algebraic Serre theorem was proved which relates the coconnectivity of the André-Quillen homology to the height of the action of certain Dwyer operations on the homotopy groups.
	www.maths.abdn.ac.uk /~stc2001/abstracts/Turner/Turner.html (235 words)

	SERRE (Site not responding. Last check: 2007-09-03)
		Search the SERRE Family Message Boards at Ancestry.com (if available).
		Search the SERRE Family Resource Center at RootsWeb.com (if available).
		Find graves of people named SERRE at Find-a-Grave.com (or add one that you know).
	www.worldhistory.com /surname/US/S/SERRE.htm (73 words)

	Riemann-Roch theorem
		An n-dimensional generalisation, the Hirzebruch-Riemann-Roch theorem, was found and proved by Friedrich Hirzebruch, as an application of characteristic classes in algebraic topology; he was much influenced by the work of Kunihiko Kodaira.
		At about the same time Jean-Pierre Serre was giving the general form of Serre duality, as we now know it.
		Finally a general version was found in algebraic topology, too.
	www.sciencedaily.com /encyclopedia/riemann_roch_theorem (1058 words)

	Présentation
		Analytic approach to the Grothendieck residue and duality theory.
		Serre's duality theorrem for cohomology with compact support of non compact complex manifolds.
		On Serre duality, à paraître au Bulletin des Sciences Mathématiques (refereed journal).
	www.math.jussieu.fr /projets/ac/Reseau/presentation.htm (2291 words)

	DC MetaData for: Tsymmetrical tensor forms and Serre duality
		Abstract: For any sheaf $\Omega^T$ of germs of T symmetrical tensor forms on a projective manifold Y there exist a Young tableau T* and an integer p such that $O_{Y(p)}$(x)$\Omega^{T}$ is dual* to $\Omega^T$.
		As an application a Lefschetztypetheorem and some vanishing theorems for the cohomology groups of complete intersections are dualized.
		The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.
	www.mathematik.uni-halle.de /reports/shadows/96-19report.html (96 words)

	[No title] (Site not responding. Last check: 2007-09-03)
		TIME: 4:10 PM (Tea at 3:45 PM) ABSTRACT: Duality is one of the fundamental concepts in mathematics.
		From the basic duality for finite dimensional vector spaces it extends in many directions: Banach spaces and topological groups in analysis, Poincare duality in topology, Serre duality in algebraic geometry, and so on.
		In the lecture I will sketch the basics of duality theory (with illuminating examples) and explain some applications in noncommutative ring theory.
	www.math.technion.ac.il /~techm/20010320161020010320yek (219 words)

	Peter Jorgensen's publications (Site not responding. Last check: 2007-09-03)
		With Anders Frankild and Srikanth Iyengar: Dualizing Differential Graded modules and Gorenstein Differential Graded Algebras, J.
		Items mentioned as being "in press" have been through their final proof reading.
		The Auslander-Reiten quiver of a Poincaré duality space, to appear in Algebr.
	www.maths.leeds.ac.uk /%7Epopjoerg/publications.html (237 words)

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