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Showing 1 to 20 of 46 for “"sheaf"”.
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Locales and sheaf representations of rings
Bibliography: leaves 46-47.
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Some Applications of Triples to Sheaf Theory
Made available in DSpace on 2014-12-09T22:17:55Z (GMT). No. of bitstreams: 1 7001014.pdf: 1784039 bytes, checksum: 1b9f05dbb477de31e2b2534efda16a57 (MD5) Previous issue date: 1969
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Sheaf Semantics in Constructive Algebra and Type Theory
In this thesis we present two applications of sheaf semantics. The first is to give constructive proof of Newton-Puiseux theorem. The second is to show the independence of Markov's principle from type theory. In the first part we study Newton-Puiseux algorithm from a constructive point of view. …
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Dimension-Theory of Sheaves of R'-Modules (R' Is the Structure Sheaf of a Commutative Ring R With 1)
Made available in DSpace on 2014-12-11T18:24:07Z (GMT). No. of bitstreams: 1 7412083.pdf: 2247917 bytes, checksum: e427d09a55ec17bc8b14a4f054481d67 (MD5) Previous issue date: 1973
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
… traces to construct a "coherent Springer sheaf" on a moduli stack of Deligne–Langlands parameters whose endomorphism algebra recovers H. In this thesis, we extend these results to Lusztig's asymptotic affine Hecke algebra J. Using work of Bezrukavnikov–Ostrik, we construct an "asymptotic …
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Torsors over Simplicial Schemes
… in a small Grothendieck site C, and let G be a sheaf of groups on C. We define a notion of G-torsor over X, generalizing a definition of Gillet, and prove that there is a bijection between the set of isomorphism classes of G-torsors over X, and the set of maps in the homotopy category of …
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Connections on conformal blocks
… space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.e. quasi-coherent sheaves with a …
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Geometry of Affine Actions
… a vertex variety, i.e. a variety whose structure sheaf is a sheaf of vertex algebras.
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On the infinitesimal theory of Chow groups
… of Bloch expresses the Chow groups as Zariski sheaf cohomology groups of algebraic K-theory sheaves on X. Bloch's formula follows from the fact that the coniveau spectral sequence for algebraic K-theory on X induces flasque resolutions of these sheaves. Algebraic cycles and algebraic K-theory …
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Torus equivariant elliptic cohomology and sigma orientations
… equivariant elliptic cohomology, which is a sheaf of $ \mathcal{ O}_{\mathcal{C}^n}$-algebras over $ \mathcal{C}^n$. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.
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An Explicit Construction of Sheaves in Context
… of supporting material necessary to connect sheaf theory with the wider mathematical contexts in which it is applied. Of particular interest is a novel presentation of the plus construction suitable for direct application to a site without first passing to the generated grothendieck …
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Surgery spaces of crystallographic groups
… groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H<sub>*</sub>(R<sup>n</sup> /Γ; L(p)) → …
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Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory
… the first cohomology group of the structure sheaf is nonzero. Such surfaces, which only exist over imperfect fields, arise as generic fibres of fibrations of singular del Pezzo surfaces in positive characteristic whose total spaces are smooth, and their study is motivated by the minimal model …
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The Frobenius direct image of line bundles and the structure of representations
… L}$($\lambda$). We study the homogeneous sheaf structure of $F\sb\*{\cal L}$($\lambda$) in the context of several celebrated representation theory problems. Specifically, our decomposition of the Frobenius direct image on the projective line provides a geometric interpretation of the …
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The overconvergent de Rham-Witt complex
… and the fact that our complex is a Zariski sheaf with sheaf cohomology equal to zero in positive degrees. (For the latter, we lift the proof from [4] and include it as an appendix.) We end with two chapters featuring independent results. In the first, we reinterpret several rings from p-adic …
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Topological Deep Learning: Graphs, Complexes, Sheaves
… a new perspective on graph models based on sheaf theory, a subfield of algebraic topology. Sheaves, which are mathematical data structures that naturally store the data attached to a topological space and its relational structure, faithfully realise the axiomatic principles of Topological …
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Gopakumar-Vafa invariant and Macdonald formula
… by Maulik-Toda in 2016 in terms of perverse sheaf. I will use this definition on the total space of canonical bundle of P2 and compute the associated invariants. I will introduce a Gopakumar-Vafa/Pandharipande-Thomas correspondence on the level of perverse sheaves, inspired by the work of …
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Geometric Langlands in prime characteristic
… stack of Gv-local systems on C. Let DBunG be the sheaf of crystalline differential operator algebra on BunG. In this thesis I construct an equivalence between the derived category D(QCoh(LocSys~v)) of quasi-coherent sheaves on some open subset LocSysov C LocSysGv and derived category D(DOunG mod) …
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Free resolutions, combinatorics, and geometry
… is closely related to the existence of an Ulrich sheaf, and our second result shows that such sheaves exist on the class of Schubert degeneracy loci. Finally, we consider the problem of classifying the possible ranks of Betti numbers for modules over a regular local ring.
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A classification of toric, folded-symplectic manifolds
… forms in terms of their induced map from the sheaf of vector fields into a distinguished sheaf of one-forms, we relate the existence of an orientation on the folding hypersurface of a fold-form to the intrinsic derivative of the contraction mapping from the tangent bundle to the cotangent …
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