R-Equivalence and Special Unitary Groups

The group of K1-zero-cycles on the second generalized Severi–Brauer variety of an algebra of index 4

“…We follow the same notational convention as [CM01], utilizing GL 1 (A), SL 1 (A), Spin(A, σ), etc., to denote the groups of F -points of the corresponding algebraic groups GL 1 (A), SL 1 (A), Spin(A, σ), etc. We suppress reference to the scheme structure and focus only on the collections of F -points, although we continue to refer to them as "algebraic groups."…”

“…Significant results include the Merkurjev-Suslin Theorem, the Milnor and Bloch-Kato Conjectures (now theorems of Orlov-Vishik-Voevodksy and VoevodskyRost-Weibel) [Voe], and Suslin's Conjecture, recently proven by Merkurjev [Mer14]. Despite these successes, a general description of Chow groups (with coefficients) remains elusive, and computations of these groups are done in various cases, e.g., [CM01,CM06,Kra,Mer95,Mer,MS92,PSZ,Swa].…”

𝑅-equivalence in spinor groups

“…By the definition of the norm map N given in [2], there is a non-empty open subset U ⊂ R L/F (G L ) and a morphism i : U → G such that for any field extension E/F the restriction to U (E) of the composition…”

“…The only known case [12] is when ind(A) is divisible by 4. In the outer case A n−1 , a simply connected algebraic group is isomorphic to the special unitary group SU(B, τ) of a central simple algebra B of dimension n 2 over a quadratic extension of F with involution τ of the second kind [9, §26]. The group of R-equivalence classes of SU(B, τ) was computed in [2].…”

Cohomological Invariants of Simply Connected Groups of Rank 3

“…We use a computation of G F /R in [3,Theorem 5.4] as the factor group 1 F / 1 F . Using a computation of algebraic K-theory of projective homogeneous varieties given in [22] we relate the group 1 F / 1 F to the factor group K 1 X 2/3 of the topological filtration on K 1 X .…”