Complex Bott Periodicity in algebraic geometry

Hannah Larson; Ravi Vakil

Complex Bott Periodicity in algebraic geometry

Algebraic Geometry 2025-09-08 v2

Authors: Hannah Larson , Ravi Vakil

Abstract

We state and prove a form of Bott periodicity (for $U(n)$ ) in an algebraic setting (so, $GL(n)$ ) which makes sense over $\mathbb{Z}$ , which also specializes to Bott periodicity in the usual sense (hence giving yet another proof of classical Bott periodicity). An appendix by B. Church gives a specialization of the constructions and results to motivic homotopy theory, which may be of independent interest.

Keywords

algebraic geometry

Cite

@article{arxiv.2411.09122,
  title  = {Complex Bott Periodicity in algebraic geometry},
  author = {Hannah Larson and Ravi Vakil},
  journal= {arXiv preprint arXiv:2411.09122},
  year   = {2025}
}

Comments

The new version contains an appendix by Ben Church giving a functor from our naive algebro-geometric homotopy category to the motivic homotopy setting, which requires some subtlety

Complex Bott Periodicity in algebraic geometry

Abstract

Keywords

Cite

Comments

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