Transfers on $\mathbb A^1$-connected components of quasi-split groups and the norm principle

Amit Hogadi; Anand Sawant

Transfers on $\mathbb A^1$-connected components of quasi-split groups and the norm principle

Algebraic Geometry 2025-12-24 v2 Algebraic Topology Group Theory K-Theory and Homology

Authors: Amit Hogadi , Anand Sawant

Abstract

We show that the sheaf of $\mathbb A^1$ -connected components of a quasi-split group over a perfect field is a strictly $\mathbb A^1$ -invariant sheaf with (Voevodsky) transfers. As a consequence, we show that the norm principle holds for any quasi-split group over a perfect field.

Keywords

$\mathbb A^1$-connected components quasi-split groups norm principle transfers Voevodsky sheaf perfect field

Cite

@article{arxiv.2512.15324,
  title  = {Transfers on $\mathbb A^1$-connected components of quasi-split groups and the norm principle},
  author = {Amit Hogadi and Anand Sawant},
  journal= {arXiv preprint arXiv:2512.15324},
  year   = {2025}
}

Comments

12 pages, v2: some inaccuracies removed, minor modifications, main results unchanged, comments are welcome

Transfers on $\mathbb A^1$-connected components of quasi-split groups and the norm principle

Abstract

Keywords

Cite

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