K-theory and G-theory of derived algebraic stacks
Adeel A. Khan
Abstract
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
Table of Contents
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K-theory and G-theory of derived algebraic stacks
Authors
Adeel A. Khan
Abstract
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
Paper Structure
This paper contains 43 sections, 72 theorems, 127 equations.
Table of Contents
- Perfect and coherent complexes
- Complexes over derived commutative rings
- Quasi-coherent, perfect, and coherent complexes
- Tensor, Hom, and inverse/direct images
- Finiteness of Tor-amplitude
- Finiteness of cohomological dimension
- Cohomological properness
- The resolution property
- Perfect stacks
- Perfectness criteria
- Continuity
- Algebraic K-theory
- Definitions
- Operations
- Projective bundles and blow-ups
- ...and 28 more sections
Key Result
Lemma 1.4
Theorems & Definitions (194)
- Definition 1.1
- Definition 1.2
- Definition 1.3
- Lemma 1.4
- proof
- Definition 1.5
- Remark 1.6
- Definition 1.7
- Remark 1.8
- Remark 1.9
- ...and 184 more