2026-09-18T20:49:52Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/301442022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Michael Hopkins.
Lurie, Jacob, 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-03-24T18:23:33Z
2006-03-24T18:23:33Z
2004
2004
http://hdl.handle.net/1721.1/30144
56017987
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes 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.
193 p.
11322244 bytes
11322052 bytes
application/pdf
application/pdf
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
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="aa7fd1f5-0f16-48be-b2fa-9950fdead084">
<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</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2004</PublicationDate>
<Authors>
<Author>
<DisplayName>Lurie, Jacob, 1977-</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>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>