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Derived algebraic geometry over En̳-rings

Author(s)
Francis, John (John Nathan Kirkpatrick)
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Michael Hopkins.
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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. http://dspace.mit.edu/handle/1721.1/7582
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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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
 
In title on t.p., double underscored "n" appears as subscript.
 
Includes bibliographical references (p. 55-56).
 
Date issued
2008
URI
http://hdl.handle.net/1721.1/43792
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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