Derived algebraic geometry

Derived algebraic geometry

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 der...

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Main Author: Lurie, Jacob, 1977-
Other Authors: Michael Hopkins.
Format: Others
Language:English
Published: Massachusetts Institute of Technology 2006
Subjects:
Mathematics.
Online Access:http://hdl.handle.net/1721.1/30144
id ndltd-MIT-oai-dspace.mit.edu-1721.1-30144
record_format oai_dc
spelling ndltd-MIT-oai-dspace.mit.edu-1721.1-301442019-05-02T16:16:53Z Derived algebraic geometry Lurie, Jacob, 1977- Michael Hopkins. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2006-03-24T18:23:33Z 2006-03-24T18:23:33Z 2004 2004 Thesis http://hdl.handle.net/1721.1/30144 56017987 eng 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 193 p. 11322244 bytes 11322052 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology
collection NDLTD
language English
format Others
sources NDLTD
topic Mathematics.
spellingShingle Mathematics.
Lurie, Jacob, 1977-
Derived algebraic geometry
description 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.
author2 Michael Hopkins.
author_facet Michael Hopkins.
Lurie, Jacob, 1977-
author Lurie, Jacob, 1977-
author_sort Lurie, Jacob, 1977-
title Derived algebraic geometry
title_short Derived algebraic geometry
title_full Derived algebraic geometry
title_fullStr Derived algebraic geometry
title_full_unstemmed Derived algebraic geometry
title_sort derived algebraic geometry
publisher Massachusetts Institute of Technology
publishDate 2006
url http://hdl.handle.net/1721.1/30144
work_keys_str_mv AT luriejacob1977 derivedalgebraicgeometry
_version_ 1719037831678001152

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