Дисертації з теми "Noncommutative derived algebraic geometry"
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Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.
Повний текст джерелаLurie, Jacob 1977. "Derived algebraic geometry." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30144.
Повний текст джерелаIncludes bibliographical references (p. 191-193).
The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.
by Jacob Lurie.
Ph.D.
Toledo, Castro Angel Israel. "Espaces de produits tensoriels sur la catégorie dérivée d'une variété." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4001.
Повний текст джерелаIn this thesis we are interested in studying derived categories of smooth projective varieties over a field. Concretely, we study the geometric and categorical information from the variety and from it's derived category in order to understand the set of monoidal structures one can equip the derived category with. The motivation for this project comes from two theorems. The first is Bondal-Orlov reconstruction theorem which says that the derived category of a variety with ample (anti-)canonical bundle is enough to recover the variety. On the other hand, we have Balmer's spectrum construction which uses the derived tensor product to recover a much larger number of varieties from it's derived category of perfect complexes as a monoidal category. The existence of different monoidal structure is in turn guaranteed by the existence of varieties with equivalent derived categories. We have as a goal then to understand the role of the tensor products in the existence (or not ) of these sort of varieties. The main results we obtained are If X is a variety with ample (anti-)canonical bundle, and ⊠ is a tensor triangulated category on Db(X) such that the Balmer spectrum Spc(Db(X),⊠) is isomorphic to X, then for any F,G∈Db(X) we have F⊠G≃F⊗G where ⊗ is the derived tensor product. We have used Toën's Morita theorem for dg-categories to give a characterization of a truncated structure in terms of bimodules over a product of dg-algebras, which induces a tensor triangulated category at the level of homotopy categories. We studied the deformation theory of these structures in the sense of Davydov-Yetter cohomology, concretely showing that there is a relationship between one of these cohomology groups and the set of associators that the tensor product can deform into. We utilise techniques at the level of triangulated categories and also perspectives from higher category theory like dg-categories and quasi-categories
Tang, Xin. "Applications of noncommutative algebraic geometry to representation theory /." Search for this dissertation online, 2006. http://wwwlib.umi.com/cr/ksu/main.
Повний текст джерелаGoetz, Peter D. "The noncommutative algebraic geometry of quantum projective spaces /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102165.
Повний текст джерелаTypescript. Includes vita and abstract. Includes bibliographical references (leaves 106-108). Also available for download via the World Wide Web; free to University of Oregon users.
Schelp, Richard Charles. "The standard model and beyond in noncommutative geometry /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
Повний текст джерелаSolanki, Vinesh. "Zariski structures in noncommutative algebraic geometry and representation theory." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45.
Повний текст джерелаFrancis, John (John Nathan Kirkpatrick). "Derived algebraic geometry over En̳-rings." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43792.
Повний текст джерелаIn title on t.p., double underscored "n" appears as subscript.
Includes bibliographical references (p. 55-56).
We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi and Lurie. The class of spaces obtained by gluing En-rings form a geometric counterpart to En-categories, which are higher topological variants of braided monoidal categories. These spaces further provide a geometric language for the deformation theory of general E, structures. A version of the cotangent complex governs such deformation theories, and we relate its values to E&-Hochschild cohomology. In the affine case, this establishes a claim made by Kontsevich. Other applications include a geometric description of higher Drinfeld centers of SE-categories, explored in work with Ben-Zvi and Nadler.
by John Francis.
Ph.D.
Di, Natale Carmelo. "Grassmannians and period mappings in derived algebraic geometry." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709191.
Повний текст джерелаMelani, Valerio. "Poisson and coisotropic structures in derived algebraic geometry." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC299/document.
Повний текст джерелаIn this thesis, we define and study Poisson and coisotropic structures on derived stacks in the framework of derived algebraic geometry. We consider two possible presentations of Poisson structures of different flavour: the first one is purely algebraic, while the second is more geometric. We show that the two approaches are in fact equivalent. We also introduce the notion of coisotropic structure on a morphism between derived stacks, once again presenting two equivalent definitions: one of them involves an appropriate generalization of the Swiss Cheese operad of Voronov, while the other is expressed in terms of relative polyvector fields. In particular, we show that the identity morphism carries a unique coisotropic structure; in turn, this gives rise to a non-trivial forgetful map from n-shifted Poisson structures to (n-1)-shifted Poisson structures. We also prove that the intersection of two coisotropic morphisms inside a n-shifted Poisson stack is naturally equipped with a canonical (n-1)-shifted Poisson structure. Moreover, we provide an equivalence between the space of non-degenerate coisotropic structures and the space of Lagrangian structures in derived geometry, as introduced in the work of Pantev-Toën-Vaquié-Vezzosi
DURIGHETTO, Sara. "Classical and Derived Birational Geometry." Doctoral thesis, Università degli studi di Ferrara, 2019. http://hdl.handle.net/11392/2488324.
Повний текст джерелаNell'ambito della geometria algebrica, lo studio delle trasformazioni birazionali e delle loro proprietà riveste un ruolo di importanza primaria. In questo, si affiancano l'approccio classico della scuola italiana che si concentra sul gruppo di Cremona e quello più moderno che utilizza strumenti come categorie derivate e decomposizioni semiortogonali. Del gruppo di Cremona Cr_n, cioé il gruppo degli automorfismi birazionali di P^n, in generale non si conosce molto e ci si concentra sul caso complesso. Si conosce un insieme di generatori solo nel caso di dimensione 2. Inoltre non é ancora nota una classicazione tramite trasformazioni di Cremona delle curve e dei sistemi lineari di P^2. Tra i casi noti ci sono: le curve irriducibili e quelle formate da due componenti irriducibili. In questa tesi ci si approccia al caso di una configurazione di d rette nel piano proiettivo. Il teorema finale fornisce condizioni necessarie o sufficienti alla contraibilità. Da un punto di vista categoriale invece, le decomposizioni semiortogonali della cat- egoria derivata di una varietà ci forniscono degli invarianti utili nello studio della varietà. Seguendo l'approccio di Clemens-Griffiths riguardante la cubica complessa di dimensione 3, si vuole caratterizzare le ostruzioni alla razionalità di una varietà X di dimensione n. L'idea è di raccogliere le componenti di una decomposizione ortog- onale che non sono equivalenti a categorie derivate di varietà di dimensione almeno n-1 e in questo modo definire quella che chiamiamo componente di Griffiths- Kuznetsov di X. In questa tesi si studia il caso delle superci geometricamante razionali su un campo arbitrario, si definisce tale componente e si mostra che essa è un invariante birazionale. Si vede anche che la componente di Griffiths-Kuznetsov è nulla solo se la supercie è razionale.
Bussi, Vittoria. "Derived symplectic structures in generalized Donaldson-Thomas theory and categorification." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:54896cc4-b3fa-4d93-9fa9-2a842ad5e4df.
Повний текст джерелаLim, Bronson. "Equivariant Derived Categories Associated to a Sum of Potentials." Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22628.
Повний текст джерелаNOCERA, Guglielmo. "A study of the spherical Hecke category via derived algebraic geometry." Doctoral thesis, Scuola Normale Superiore, 2022. https://hdl.handle.net/11384/125742.
Повний текст джерелаKhan, Adeel [Verfasser], and Marc [Akademischer Betreuer] Levine. "Motivic homotopy theory in derived algebraic geometry / Adeel Khan. Betreuer: Marc Levine." Duisburg, 2016. http://d-nb.info/1113534451/34.
Повний текст джерелаTiger, Norkvist Axel. "Morphisms of real calculi from a geometric and algebraic perspective." Licentiate thesis, Linköpings universitet, Algebra, geometri och diskret matematik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-175740.
Повний текст джерелаIckekommutativ geometri har under de senaste fyra decennierna blivit ett etablerat forskningsområde inom matematiken. Nya idéer och koncept utvecklas i snabb takt, och en viktig fysikalisk tillämpning av teorin är inom kvantteorin. Denna avhandling kommer att fokusera på ett derivationsbaserat tillvägagångssätt inom ickekommutativ geometri där ramverket real calculi används, vilket är ett relativt direkt sätt att studera ämnet på. Eftersom analogin mellan real calculi och klassisk Riemanngeometri är intuitivt klar så är real calculi användbara när man undersöker hur klassiska koncept inom Riemanngeometri kan generaliseras till en ickekommutativ kontext. Denna avhandling ämnar att klargöra vissa algebraiska aspekter av real calculi genom att introducera morfismer för dessa, vilket möjliggör studiet av real calculi på en strukturell nivå. I synnerhet diskuteras real calculi över matrisalgebror från både ett algebraiskt och ett geometriskt perspektiv. Morfismer tolkas även geometriskt, vilket leder till en ickekommutativ teori för inbäddningar. Som ett exempel blir den ickekommutativa torusen minimalt inbäddad i den ickekommutativa 3-sfären.
Byrnes, Sean. "Some computational and geometric aspects of generalized Weyl algebras /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18765.pdf.
Повний текст джерелаCalabrese, John. "In the hall of the flop king : two applications of perverse coherent sheaves to Donaldson-Thomas invariants." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b96b2bdd-8c79-4910-8795-f147bc8b2d16.
Повний текст джерелаBach, Samuel. "Formes quadratiques décalées et déformations." Thesis, Montpellier, 2017. http://www.theses.fr/2017MONTS013/document.
Повний текст джерелаThe classical L-theory of a commutative ring is built from the quadratic forms over this ring modulo a lagrangian equivalence relation.We build the derived L-theory from the n-shifted quadratic forms on a derived commutative ring. We show that forms which admit a lagrangian have a standard form. We prove surgery results for this derived L-theory, which allows to reduce shifted quadratic forms to equivalent simpler forms. We compare classical and derived L-theory.We define a derived stack of shifted quadratic forms and a derived stack of lagrangians in a form, which are locally algebraic of finite presentation. We compute tangent complexes and find smooth points. We prove a rigidity result for L-theory : the L-theory of a commutative ring is isomorphic to that of any henselian neighbourhood of this ring.Finally, we define the Clifford algebra of a n-shifted quadratic form, which is a deformation as E_k-algebra of a symmetric algebra. We prove a weakening of the Azumaya property for these algebras, in the case n=0, which we call semi-Azumaya. This property expresses the triviality of the Hochschild homology of the Serre bimodule
Prabhu-Naik, Nathan. "Tilting bundles and toric Fano varieties." Thesis, University of Bath, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690721.
Повний текст джерелаFeyzbakhsh, Soheyla. "Bridgeland stability conditions, stability of the restricted bundle, Brill-Noether theory and Mukai's program." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31485.
Повний текст джерелаMarangoni, Davide. "On Derived de Rham cohomology." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0095.
Повний текст джерелаThe derived de Rham complex has been introduced by Illusie in 1972. Its definition relies on the notion of cotangent complex. This theory seems to have been forgot until the recents works by Be˘ılinson and Bhatt, who gave several applications, in particular in p-adic Hodge Theory. On the other hand, the derived de Rham cohomology has a crucial role in a conjecture by Flach-Morin about special values of zeta functions for arithmetic schemes. The aim of this thesis is to study and compute the Hodge completed derived de Rham complex in some cases
Schmidt, Benjamin. "Stability Conditions on Threefolds and Space Curves." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460542777.
Повний текст джерелаLam, Yan Ting. "Calabi-Yau categories and quivers with superpotential." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:20e38c16-e8c7-4ed4-85c9-e22ee6f6e467.
Повний текст джерелаHennion, Benjamin. "Formal loops spaces and tangent Lie algebras." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS160/document.
Повний текст джерелаIf M is a symplectic manifold then the space of smooth loops C(S^1,M) inherits of a quasi-symplectic form. We will focus in this thesis on an algebraic analogue of that result.In their article, Kapranov and Vasserot introduced and studied the formal loop space of a scheme X. It is an algebraic version of the space of smooth loops in a differentiable manifold.We generalize their construction to higher dimensional loops. To any scheme X -- not necessarily smooth -- we associate L^d(X), the space of loops of dimension d. We prove it has a structure of (derived) Tate scheme -- ie its tangent is a Tate module: it is infinite dimensional but behaves nicely enough regarding duality.We also define the bubble space B^d(X), a variation of the loop space.We prove that B^d(X) is endowed with a natural symplectic form as soon as X has one.To prove our results, we develop a theory of Tate objects in a stable infinity category C. We also prove that the non-connective K-theory of Tate(C) is the suspension of that of C, giving an infinity categorical version of a result of Saito.The last chapter is aimed at a different problem: we prove there the existence of a Lie structure on the tangent of a derived Artin stack X. Moreover, any quasi-coherent module E on X is endowed with an action of this tangent Lie algebra through the Atiyah class of E. This in particular applies to not necessarily smooth schemes X
DASTI, LORENZO. "A COMPARISON BETWEEN GEOMETRIC QUASI-FUNCTORS AND FOURIER-MUKAI FUNCTORS." Doctoral thesis, Università degli Studi di Milano, 2023. https://hdl.handle.net/2434/953452.
Повний текст джерелаIn this PhD thesis I have delt with the relationship between the most important class of functors between derived categories, i.e. Fourier-Mukai functors, and quasi-functors which are the morphisms in the localization Hqe of the category of dg categories with respect to quasi-equivalences. To be more precise: let X and Y be two smooth and proper schemes over a field. I have defined an explicit bijection between the isomorphism class of the triangulated category of perfect complexes over X×Y and the set of morphism in Hqe between two (fixed) dg enhancemenst of the categories of perfect complexes over X and over Y , respectively. Moreover, I have showed that this bijection associates to the dg lift of a Fourier-Mukai functor the isomorphism class of its kernel, giving a positive answer to a conjecture of Toën.
Wallbridge, James. "Higher Tannaka duality." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1440/.
Повний текст джерелаIn this thesis we prove a Tannaka duality theorem for (infini, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (infini, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toën. We also describe three applications of our theory : perfect complexes and that of both motives and its non-commutative analogue due to Kontsevich
Pippi, Massimo. "Catégories des singularités, factorisations matricielles et cycles évanescents." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30049.
Повний текст джерелаThe aim of this thesis is to study the dg categories of singularities Sing(X, s) of pairs (X, s), where X is a scheme and s is a global section of some vector bundle over X. Sing(X, s) is defined as the kernel of the dg functor from Sing(X0) to Sing(X) induced by the pushforward along the inclusion of the (derived) zero locus X0 of s in X. In the first part, we restrict ourselves to the case where the vector bundle is trivial. We prove a structure theorem for Sing(X, s) when X = Spec(B) is affine. Roughly, it tells us that every object in Sing(X, s) is represented by a complex of B-modules concentrated in n + 1 consecutive degrees (if s epsilon Bn). By specializing to the case n = 1, we generalize Orlov's theorem, which identifies Sing(X, s) with the dg category of matrix factorizations MF(X, s), to the case where s epsilon OX(X) is not flat. In the second part, we study the l-adic cohomology of Sing(X, s) (as defined by A. Blanc - M. Robalo - B. Toën and G. Vezzosi) when s is a global section of a line bundle. In order to do so, we introduce the l-adic sheaf of monodromy-invariant vanishing cycles. Using a theorem of D. Orlov generalized by J. Burke and M. Walker, we compute the l-adic realization of Sing(Spec(B), (f1 ,..., fn)) for (f1 ,..., fn) epsilon Bn. In the last chapter, we introduce the l-adic sheaves of iterated vanishing cycles of a scheme over a discrete valuation ring of rank 2. We relate one of these l-adic sheaves to the l-adic realization of the dg category of singularities of the fiber over a closed subscheme of the base
Brav, Christopher. "Tilting objects in derived categories of equivariant sheaves." Thesis, 2008. http://hdl.handle.net/1974/1408.
Повний текст джерелаThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-09-04 14:42:25.099
Safronov, Pavel. "Geometry of integrable hierarchies and their dispersionless limits." Thesis, 2014. http://hdl.handle.net/2152/24818.
Повний текст джерелаtext
Potashnik, Natasha. "Derived Categories of Moduli Spaces of Semistable Pairs over Curves." Thesis, 2016. https://doi.org/10.7916/D8H99542.
Повний текст джерелаRoy, Arya. "Towards A Stability Condition on the Quintic Threefold." Diss., 2010. http://hdl.handle.net/10161/2976.
Повний текст джерелаIn this thesis we try to construct a stability condition on the quintic threefold. We have not succeeded in proving the existence of such a stability condition. However we have constructed a stability condition on a quotient category of projective space that approximates the quintic. We conjecture the existence of a stability condition on the quintic threefold generated by spherical objects and explore some consequences.
Dissertation
Kratsios, Anastasis. "Bounding The Hochschild Cohomological Dimension." Thèse, 2014. http://hdl.handle.net/1866/12814.
Повний текст джерелаThe aim of this master’s thesis is two-fold. Firstly to develop and interpret the low dimensional Hochschild cohomology of a k-algebra and secondly to establish a lower bound for the Hochschild cohomological dimension of a k-algebra; showing that nearly no commutative k-algebra is quasi-free.
Wallbridge, James. "Higher Tannaka duality." Thesis, 2011. http://hdl.handle.net/2440/69436.
Повний текст джерелаThesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2011
Lowrey, Parker Eastin. "Autoequivalences, stability conditions, and n-gons : an example of how stability conditions illuminate the action of autoequivalences associated to derived categories." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-986.
Повний текст джерелаtext
Bruce, Chris. "C*-algebras from actions of congruence monoids." Thesis, 2020. http://hdl.handle.net/1828/11689.
Повний текст джерелаGraduate