Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of degree 4

Patrick K. McFaddin

doi:10.1016/j.jpaa.2018.09.017

paper

Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of degree 4

arXiv:1703.03826 · doi:10.1016/j.jpaa.2018.09.017

Abstract

We compute the group of $K_{1}$ -zero-cycles on the second generalized involution variety for an algebra of degree 4 with symplectic involution. This description is given in terms of the group of multipliers of similitudes associated to the algebra with involution. Our method utilizes the framework of Chernousov and Merkurjev for computing $K_{1}$ -zero-cycles in terms of $R$ -equivalence classes of prescribed algebraic groups. This gives a computation of $K_{1}$ -zero-cycles for some homogeneous varieties of type $C_{2}$ .

arXiv commentAn error spotted in a previous version was corrected but makes the main result less general. This also necessitated a change to the title. 11 pages, comments welcome!

References in corpus (1)

The group of $K_{1}$ -zero-cycles on the second generalized Severi-Brauer variety of an algebra of index 4