Algebraic stacks
نویسنده
چکیده
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.
منابع مشابه
A note on group actions on algebraic stacks
we give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.
متن کاملK-Theory and G-Theory of DG-stacks
In this paper, we establish results of a basic nature for the the K-theory and G-theory of algebraic stacks, i.e. Artin stacks. At the same time, we enlarge the framework a bit more so that these results not only hold for stacks, but also for what are called dg-stacks, i.e. algebraic stacks where the usual structure sheaf is replaced by a sheaf of dgas.
متن کاملNotes on algebraic stacks
1 Moduli problems, spaces, and stacks. Vector bundles and K-theory 3 1.1 Some category theory . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Back to moduli spaces . . . . . . . . . . . . . . . . . . . . . . 4 1.3 The way out of the problem . . . . . . . . . . . . . . . . . . . 7 1.4 Algebraic stacks and moduli of vector bundles . . . . . . . . . 7 1.5 K-theory of schemes . . . . . . . . . . ...
متن کاملCharacterizing Algebraic Stacks
We extend the notion of algebraic stack to an arbitrary subcanonical site C. If the topology on C is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic n-stacks. We also compare different sites...
متن کاملDerived Categories of Stacks
In this chapter we write about derived categories associated to algebraic stacks. This means in particular derived categories of quasi-coherent sheaves, i.e., we prove analogues of the results on schemes (see Derived Categories of Schemes, Section 1) and algebraic spaces (see Derived Categories of Spaces, Section 1). The results in this chapter are different from those in [LMB00] mainly because...
متن کامل