Derived algebraic geometry

Author(s)
Lurie, Jacob, 1977-
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Michael Hopkins.
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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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
 
Includes bibliographical references (p. 191-193).
 
Date issued
2004
URI
http://hdl.handle.net/1721.1/30144
Department
Massachusetts Institute of Technology. Dept. of Mathematics.
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.
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