Subtle characteristic classes for Spin-torsors

Tanania, Fabio (2021): Subtle characteristic classes for Spin-torsors. In: Mathematische Zeitschrift, Vol. 301, No. 1: pp. 41-74

Abstract

Extending (Smirnov and Vishik, Subtle Characteristic Classes, arXiv:1401.6661), we obtain a complete description of the motivic cohomology with Z/2-coefficients of the Nisnevich classifying space of the spin group Spinn associated to the standard split quadratic form. This provides us with very simple relations among subtle Stiefel-Whitney classes in the motivic cohomology of Cech simplicial schemes associated to quadratic forms from I-3, which are closely related to Spinn-torsors over the point. These relations come from the action of the motivic Steenrod algebra on the second subtle Stiefel-Whitney class. Moreover, exploiting the relation between Spin(7) and G(2), we describe completely the motivic cohomology ring of the Nisnevich classifying space of G(2). The result in topology was obtained by Quillen (Math Ann 194:197-212, 1971).

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0025-5874
• Language: English