Speaker: Bertrand Toen (U. Montpellier)
Title: Lecture 3: Moduli 2: moduli of non simple objects and higher stacks.
Date (JST): Thu, Apr 15, 2010, 15:30 - 17:00
Place: Seminar Room A
Abstract: Lecture 2-3: We discuss the general problem of constructing an algebraic moduli of objects in derived categories. We will present a first solution to this problem by stating the existence of an algebraic space of compact and simple objects in a nice enough dg-category. We provide applications of the existence a such a moduli space in the study of derived category of algebraic varieties. In a second part, we study the existence of a moduli space for non necessarily simple objects, and state the existence of an algebraic (higher) stack classifying all compact objects in a nice dg-category. As an application we present the construction of Hall algebras in the derived setting by means of geometric methods.
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