| Summary: | 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.
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