Stable points on algebraic stacks

Sheaves on Algebraic Stacks

Notes 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 . . . . . . . . . . ...

Sheaves on Algebraic Stacks

Sheaves on Algebraic Stacks

Algebraic stacks

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.