Suslin’s conjecture on the reduced Whitehead group of a simple algebra

Merkurjev, Alexander

doi:10.1090/jams/850

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Cited by 3 publications

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

McFaddin

2017

Journal of Algebra

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Abstract. In this manuscript, it is shown that the group of K 1 -zero-cycles on the second generalized Severi-Brauer variety of an algebra A of index 4 is given by elements of the group K 1 (A) together with a square-root of their reduced norm. Utilizing results of Krashen concerning exceptional isomorphisms, we translate our problem to the computation of cycles on involution varieties. Work of Chernousov and Merkurjev then gives a means of describing such cycles in terms of Clifford and spin groups and corresponding R-equivalence classes. We complete our computation by giving an explicit description of these algebraic groups.

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