A remark on connective K-theory

Karpenko, Nikita A.

doi:10.1016/j.jalgebra.2020.06.015

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…induced by the inclusion M n−i+1 (X) ⊂ M (X); for i ≤ 2 the map ψ i X is an isomorphism [Kar20,Remark A.6]. In general, if we identify K(X) = G(X) by the canonical map, then the K(X)-module structure on CK i (X) is related to the ring structure of CK(X) via ψ i X .…”

Section: Connective K-theorymentioning

confidence: 99%

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior

Mackall

2021

Doc. Math.

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We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective K-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for an arbitrary Severi-Brauer variety.

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Section: Connective K-theorymentioning

confidence: 99%

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior

Mackall

2021

Doc. Math.

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“…By [12,Theorem 3.1], the statement of Conjecture 1.2 for a given G is equivalent to absence of torsion in the connective K-theory of X. Also note that by [8,Lemma 4.2], Conjecture 1.2 is equivalent to the same statement with the Borel subgroups replaced by any conjugacy class of special parabolic subgroups in G, where an algebraic group P is called special if any P -torsor over any base field extension is trivial.…”

Section: Introductionmentioning

confidence: 99%

Yagita’s counter-examples and beyond

Baek

Karpenko

2023

Arkiv För Matematik

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A conjecture on a relationship between the Chow and Grothendieck rings for the generically twisted variety of Borel subgroups in a split semisimple group G, stated by the second author, has been disproved by Nobuaki Yagita in characteristic 0 for G=Spin(2n+1) with n=8 and n=9. For n=8, the second author provided an alternative simpler proof of Yagita's result, working in any characteristic, but failed to do so for n=9. This gap is filled here by involving a new ingredient -Pieri type K-theoretic formulas for highest orthogonal grassmannians. Besides, a similar counter-example for n=10 is produced. Note that the conjecture on Spin(2n+1) holds for n up to 5; it remains open for n=6, n=7, and every n≥11.

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A remark on connective K-theory

Cited by 2 publications

References 9 publications

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior

Yagita’s counter-examples and beyond

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