2026-09-19T10:30:18Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/437922022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Michael Hopkins.
Francis, John (John Nathan Kirkpatrick)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2008-12-11T18:28:22Z
2008-12-11T18:28:22Z
2008
2008
http://hdl.handle.net/1721.1/43792
261341912
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).
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.
56 p.
eng
Massachusetts Institute of Technology
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
Mathematics.
Derived algebraic geometry over En̳-rings
Thesis
application/pdf
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="9537f4fb-1b03-4a43-9b28-228318e43edc">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Derived algebraic geometry over En̳-rings</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2008</PublicationDate>
<Authors>
<Author>
<DisplayName>Francis, John (John Nathan Kirkpatrick)</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>