Corpus ID: 119165876

Constructing the Unstable Motivic Homotopy Category Using $(\infty,1)$-Categories

@article{Brazelton2018ConstructingTU,
  title={Constructing the Unstable Motivic Homotopy Category Using \$(\infty,1)\$-Categories},
  author={T. Brazelton},
  journal={arXiv: Algebraic Topology},
  year={2018}
}
  • T. Brazelton
  • Published 28 September 2018
  • Mathematics
  • arXiv: Algebraic Topology
This is an expository paper providing an overview of the unstable motivic homotopy category using the theory of $(\infty,1)$-categories. In this paper, we examine two constructions in the literature and discuss their equivalence. 

References

SHOWING 1-9 OF 9 REFERENCES
K-theory and the bridge from motives to noncommutative motives
Abstract In this work we present a new approach to the theory of noncommutative motives and use it to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work isExpand
Norms in motivic homotopy theory
If $f : S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes : \mathcal{H}_{\bullet}(S')\to \mathcal{H}_{\bullet}(S)$, whereExpand
A1-homotopy theory of schemes
© Publications mathématiques de l’I.H.É.S., 1999, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
Adv
  • Math., 269:399–550,
  • 2015
A1-homotopy theory
volume 95 of Proc
  • Sympos. Pure Math., pages 305–370. Amer. Math. Soc., Providence, RI,
  • 2017
volume 170 of Annals of Mathematics Studies
  • Princeton University Press, Princeton, NJ,
  • 2009
Adv
  • Math., 164(1):144–176,
  • 2001