Serre duality is the analog for coherent sheaf cohomology of poincare duality in topology, with the canonical line bundle replacing the orientation sheaf. If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact web. Since the sphitchin system is the xedpointset of the serre duality on the glhitchin system, we can determine the integrable equations corresponding to the sp. Introduction this work concerns the modular representation theory of. The first goal of this paper is to describe the serre duality on ag explicitly.
Serre duality, abels theorem, and jacobi inversion for. Noetherian hereditary categories satisfying serre duality. Skoruppa sko85, sko08 and serre stark ss77, along with serre duality, to handle weights 12 and 32 in many cases, and eliminate weight one by imposing parity restrictions analogous to restricting to representations of psl 2z versus odd representations of sl 2z. University of groningen serre duality for rigid analytic. Just upload files you want to join together, reorder them with draganddrop if you need and click join files button to merge the documents. Two curves are isomorphic to each other if their jacobians are so. If d x is a relatively compact subset of x,weconsiderthe. For the second, we note that since x is geometric, p is an a. As a consequence we obtain a classification of saturated noetherian hereditary categories. Lecture 25 proof of serre duality mit opencourseware.
A complex k3 surface is a compact connected 2dimensional complex manifold xsuch that. As indicated, some notes spanned more than one lecture, and some lectures covered topics from more than one set of lecture notes. On the hausdorff property of some dolbeault cohomology groups. Hodge theory problem sheet 1 these exercises were pulled from the following books. Item b above suggests that the weight2 hodge structure of x might capture much of the geometry of x. On serre duality for compact homologically smooth dg algebras. The successful approach for stein spaces is the basis for this paper. Finally, if xis a nonsingular variety over an algebraically closed. In practice it is useful to know when the relative duality map is an isomorphism. We prove the serre duality theorem for the noncommutative projective scheme proj awhen ais a graded noetherian pi ring or a graded noetherian asgorenstein ring. Notes on geometric langlands harvard department of mathematics. Quantum riemannroch, lefschetz and serre 17 as multiplication in the cohomology algebra by i a. Duality for finite morphisms in this section, x and y are noetherian schemes and f. In this paper we will formulate the duality for the cauchyriemann complex in various function spaces and use the duality to study the hausdorff property of dolbeault cohomology groups.
The serre duality for a holomorphic vector bundle over a compact, complex manifold still holds over a compact. It relates sheaf cohomology groups on nonsingular projective algebraic varieties. For associative noetherian ngraded algebra a noncommutative analogue of serre duality on proja is formulated and proved. In this paper, we describe a serre functor on the category of perfect modules over an arbitrary compact and smooth dg algebra and use it to prove the existence of a nondegenerate pairing on the hochschild homology of the dg algebra. This duality induces the generalized serre functor on t, which is a linear triangle equivalence between two thick triangulated subcategories of t. Professor joyce complex manifolds and kahler geometry mondays 10am 12pm in room vc1, the maths institute, oxford, starting on monday 20th january and finishing on monday 9th march. It is more general than the earlier versions 4, 29. On serreduality for coherent sheaves on rigidanalytic spaces. We introduce sheaves and sheaf cohomology and use them to prove the riemannroch theorem and serre duality. Joseph lipman, notes on derived functors and grothendieck duality, in.
Let x be an integral projective scheme of dimension n over a perfect eld k. Because of the adjoint property of f 1, we have a morphismf 1o y. An algebraic proof of riemannroch ravi vakil contents 1. Serre duality manoj kummini we give a proof of the serre duality theorem using duality for. Many thanks to justin walker for improving the class notes immeasurably. First, these shadow prices give us directly the marginal worth of an additional unit of any of the resources. This establishes a duality between the cohomology of a. Finally, we explain in broad strokes an analogy between brauer classes on k3 surfaces and torsion points on elliptic curves. This article was processed by the author using the itex style file cljourl from. On classical riemann roch and hirzebruchs generalization 0. Pdf noncommutative generalization of serre duality. Serre functor, except that it is not in general an autoequivalence.
Brian conrad, grothendieck duality and base change, springer lec. The goal of this article is to motivate and describe how gromovwitten theory can and has provided tools to understand the moduli space of curves. To change the order of your pdfs, drag and drop the files as you want. In order to keep the statements and the proofs reasonable we make the restrictions y is affinoid and x y is smooth and proper. You can merge pdfs or a mix of pdf documents and other files. Let x be a complex manifold with finitely many ends such that each end is either qconcave or nqconvex. For an html and pdf or ppt file with the same name, the html is an exposition. What links here related changes upload file special pages permanent link page information wikidata item cite this page. How to merge pdfs and combine pdf files adobe acrobat dc. Pdf documents are often used because they help preserve the original content of the document, but this can make splitting the file up a little more difficult than other document formats. They discuss the riemannroch theorem and serre duality. The serre duality for holomorphic vector bundles over. This generalized duality induces the generalized serre functor of t, which is a linear triangle equivalence between certain thick triangulated subcategories of t.
As a side result we show that when our hereditary categories have no nonzero projectives or injectives, then the serre duality property is equivalent to the existence of almost split sequences. Serre duality, abels theorem, and jacobi inversion for supercurves over a thick superpoint. We will call this set of data the generalized serre duality on c. It is based on earlier works in several complex variables, however, we will observe it algebraically. In the present paper, we introduce a notion of generalized serre duality on a hom. Serre duality for noncommutative p1bundles article pdf available in transactions of the american mathematical society 3574 november 2002 with reads how we measure reads. Then, there is a unique up to unique isomor phismcoherentsheaf. Maximal frattini quotients of ppoinare duality groups, at davidson ams meeting on 030307, davidson n. Dg algebras, arising in this way, have to satisfy some compactness and smoothness conditions. Note that by serre duality, the two statements above are equivalent. Rearrange individual pages or entire files in the desired order. Serre functors play an important role in reconstruction of a variety from its derived category of coherent sheaves 6. A separation theorem and serre duality for the dolbeault cohomology christine laurentthi6baut and jfirgen leiterer abstract.
We investigatesome basic propertiesof finslermetricson holomorphic vector bundles, in the perspective of obtaining geometric versions of the serre duality theorem. In the associated long exact sequence, we know by the lefschetz hyperplane theorem. The general class of weil representations that we consider in this paper. Not all papers that appear in the list of references are ready to be posted, but most of them exist in one form or another, and youre. Duality in linear programming 4 in the preceding chapter on sensitivity analysis, we saw that the shadowprice interpretation of the optimal simplex multipliers is a very useful concept. I have heard tangential statements from some people that there is indeed some connection between the two. Complex manifolds and kahler geometry prof joyce 16 mt. Merge pdf files combine pdfs in the order you want with the easiest pdf merger available. Sym i v for i 0 we will give two proofs for the theorem and the corollary. For hypersurfaces we recover the residue formula of the string theorists kapustin and li.
We carefully develop the theory of serre duality and dualizing. Serre duality or sd prove that h1d is isomorphic to the dual space lkd, where k is the divisor of a differential form on x. The winter quarter will cover more scheme theory, sheaf cohomology, algebraic curves, riemannroch, serre duality. Precise connection between poincare duality and serre duality. Find materials for this course in the pages linked along the left. Observe that the category chas serre duality in the sense of 7 if and only if r c l. Luckily given a right serre functor there is a formal procedure to invert it so as to obtain a true serre functor theorem ii.
It turns out that the commutator isomorphism for any klinear autoequivalence on a, studied in 11, plays a central role. We study serre duality in the singularity category of an isolated gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. It has been observed and wellknown that there is a strong analogy between the behavior of the number. Coherent duality i give the statement of coherent duality and recall how it generalises serre duality. An application of serregrothendieck duality theorem to local cohomology. Hodge decomposition for curves let x be a compact connected complex curve. We refer to for various approaches to this important result. In this paper a duality theory for morphism x y of rigid analytic spaces over some nonarchimedean valued complete field k is developed.
Another rapidly developing area where serre functors. Graduate lecture course, 16 lectures, spring term 2020. If q serre files pendant une evacuation book pdf free download link or read online here in pdf. An application of serregrothendieck duality theorem to. The notes below were discussed in the lectures specified in the table. More precisely, if d is a positive divisor of distinct points, i. Serre duality is a special case of the duality called the coherent duality in a much general setting. Residues and duality for singularity categories of. The serre duality theorem is also true in complex geometry more generally, for compact complex manifolds that are not necessarily projective complex algebraic varieties.
We now sketch how the serre duality theorem iii, 7. Request pdf serre duality for khovanovrozansky homology we prove that the full twist is a serre functor in the homotopy category of type a soergel bimodules. The serre duality theorem for holomorphic vector bundles over a strongly pseudoconvex manifold. All books are in clear copy here, and all files are secure so dont worry about it. Sheaves and functions modulo p homepages of uvafnwi staff. Of course, the restriction on the classical serre duality are rather severe. Serre duality, abels theorem, and jacobi inversion for supercurves. Click add files and select the files you want to include in your pdf. We will show, using abels theorem, that the serre duality is simply the formal adjoint operation on the pseudodi erential operators. In algebraic geometry, a branch of mathematics, serre duality is a duality for the coherent sheaf. By borel serre duality, if torsionfree, the steinberg module is. Serre duality for noncommutative algebras 5 theorem 3. Pdf joiner allows you to merge multiple pdf documents and images into a single pdf file, free of charge. This yields a hereditary abelian category repfq which satis es serre duality.
Vector bundles and brillnoether theory 147 theorem 1. We introduce a notion of generalized serre duality on a hom. Finally serres same computation shows that the graded module in 7. Computations in the topology of locally symmetric spaces. Serre duality for khovanovrozansky homology request pdf. Click, drag, and drop to reorder files or press delete to remove any content you dont want. The statements of poincare duality for manifolds and serre duality for coherent sheaves on algebraic varieties or analytic spaces look tantalizingly similar. A fundamental result in the theory of complex manifolds is serres duality the orem. On the other hand, to any quadratic algebra ewe may associate its quadratic dual algebra e we show that the algebras aand bare dual to each other in both of these senses. Pseudoconvexconcave duality and regularization of currents. Poles of instantons and jumping lines of algebraic vector bundles on p bymotohicovulase research institute for mathematical science.
The serre duality for holomorphic vector bundles over strongly pseudo convex cr manifolds 19 we call a s. Here is another proof of serre duality for curves, due to serre. In particular, if xis cohenmacaulay, it gives a duality theorem just like the one on projective space. Serre duality and applications 3 furthermore, if g is a sheaf of o ymodules, then f 1g is a f 1o ymodule. In fact, we have that for any f2 qcox, f f is an f oxmodule. Let us explain the sense in which an algebraic k3 surface is also a complex k3 surface. Pseudoconvexconcave duality and regularization of currents jeanpierre demailly to the memory of michael schneider abstract. These notes on spectral sequences and cech cohomology were not. Read online role des guides et serre files pendant une evacuation book pdf free download link book now. Here, thick subcategories mean subcategories which are closed under direct summands. The main purpose of this article is to prove a serreduality theorem for coherent. Has a completely group theoretic formulation of the main conjecture of modular towers, and examples that are serious tests for the strong torsion conjecture. On the other hand, to any quadratic algebra ewe may associate its quadratic dual algebra e.
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