M ay 2 00 9 MOTIVIC WEIGHT COMPLEXES FOR ARITHMETIC VARIETIES

@inproceedings{Gillet2009MA2,
  title={M ay 2 00 9 MOTIVIC WEIGHT COMPLEXES FOR ARITHMETIC VARIETIES},
  author={Henri Gillet},
  year={2009}
}
Introduction 2 1. Stacks 5 1.1. Quotient stacks 5 1.2. Resolution of singularities 6 2. Hypercovers 7 2.1. Simplicial objects and coskeleta 7 2.2. Hypercovers and right lifting 11 2.3. Hypercovers of schemes and stacks 14 2.4. Compactification of simplicial varieties 16 3. Homological descent 20 4. Review of K-theory 27 4.1. The homology theory associated to G-theory 27 4.2. G-theory of stacks 28 5. Weight complexes for varieties and stacks 31 5.