English

Milnor-Witt Cycle Modules

Algebraic Geometry 2020-05-04 v3

Abstract

We generalize Rost's theory of cycle modules using Milnor-Witt K-theory instead of the classical Milnor K-theory. We obtain a (quadratic) setting to study general cycle complexes and their (co)homology groups. The usual constructions are developed: proper pushfoward, (essentially) smooth pullback, long exact sequences, (coniveau) spectral sequences and products, as well as the homotopy invariance property; in addition, Gysin morphisms for lci maps are constructed. We prove an adjunction theorem linking our theory to Rost's.

Keywords

Cite

@article{arxiv.1811.12163,
  title  = {Milnor-Witt Cycle Modules},
  author = {Niels Feld},
  journal= {arXiv preprint arXiv:1811.12163},
  year   = {2020}
}

Comments

Accepted for publication in Journal of Pure and Applied Algebra

R2 v1 2026-06-23T06:25:10.942Z