Transfers on \mathbb A¹-connected components of quasi-split groups and the norm principle

2025/12/17 by Hogadi, Amit, Sawant, Anand
#14F42 #20G15 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2512.15324

Abstract

We show that the sheaf of \mathbb A¹-connected components of a quasi-split group over a perfect field is a strictly \mathbb A¹-invariant sheaf with (Voevodsky) transfers. As a consequence, we show that the norm principle holds for any quasi-split group over a perfect field.

Citations

• Hensel's lemma for the norm principle for spinor groups
• The norm principle for type D_n groups over complete discretely valued fields

Related

• Strong \mathbb A¹-invariance of \mathbb A¹-connected components of reductive algebraic groups
• Transfers for non-stable K₁-functors of classical type
• Tilting sheaves for real groups and Koszul duality
• A converse theorem for quasi-split even special orthogonal groups over finite fields
• Naive vs. genuine A¹-connectedness