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Derived algebraic geometry over En̳-rings

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dc.contributor.advisor Michael Hopkins. en_US Francis, John (John Nathan Kirkpatrick) en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2008-12-11T18:28:22Z 2008-12-11T18:28:22Z 2008 en_US 2008 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. en_US
dc.description In title on t.p., double underscored "n" appears as subscript. en_US
dc.description Includes bibliographical references (p. 55-56). en_US
dc.description.abstract 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. en_US
dc.description.statementofresponsibility by John Francis. en_US
dc.format.extent 56 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Derived algebraic geometry over En̳-rings en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 261341912 en_US

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