Motivic spheres and the image of the Suslin-Hurewicz map

• 成果类型: Article
• 署名作者: Asok, Aravind; Fasel, Jean; Williams, Ben
• 署名单位: University of Southern California; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of British Columbia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00907-z
• 发表日期: 2020
• 页码: 39-73
• 关键词: a(1)-homotopy theory; vector-bundles; K-THEORY; cohomological invariants; milnors conjecture; linear-group; HOMOLOGY; sequence

摘要

We show that an old conjecture of A. A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree n to Milnor K-theory in degree n admits an interpretation in terms of unstable A1-homotopy sheaves of the general linear group. Using this identification, we establish Suslin's conjecture in degree 5 for infinite fields having characteristic unequal to 2 or 3. We do this by linking the relevant unstable A1-homotopy sheaf of the general linear group to the stable A1-homotopy of motivic spheres.