Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map

• 成果类型: Article
• 署名作者: Roendigs, Oliver
• 署名单位: University Osnabruck
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01179-4
• 发表日期: 2023
• 页码: 1161-1194
• 关键词: a(1)-homotopy theory; bundles

摘要

The endomorphism ring of the projective plane over a field F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy category than in Voevodsky's derived category of motives. In particular, it is not commutative precisely if there exists a square in F which does not admit a sixth root. A byproduct of these computations is a proof of Suslin's conjecture on the Suslin-Hurewicz homomorphism from Quillen to Milnor K-theory in degree four, based on work of Asok et al. (Invent Math 219:39-73, 2020).