English

The universal six-functor formalism

Algebraic Geometry 2023-08-08 v4 Algebraic Topology Category Theory K-Theory and Homology

Abstract

We prove that Morel-Voevodsky's stable A1\mathbb{A}^1-homotopy theory affords the universal coefficient system, giving rise to Grothendieck's six operations.

Cite

@article{arxiv.2009.13610,
  title  = {The universal six-functor formalism},
  author = {Brad Drew and Martin Gallauer},
  journal= {arXiv preprint arXiv:2009.13610},
  year   = {2023}
}

Comments

50 pages; v2: new introduction, other minor changes; v3: accepted version; v4: corrects a small mistake in published version

R2 v1 2026-06-23T18:51:37.281Z