Murthy’s conjecture on 0-cycles

Krishna, Amalendu

doi:10.1007/s00222-019-00871-8

Cited by 9 publications

(21 citation statements)

References 67 publications

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“…The second key ingredient in the proof of Theorem 0.5 is the following affine Roitman torsion theorem for 0-cycles. This is an old conjecture of Murthy [30] and is now a theorem [25,Corollary 7.6].…”

Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 83%

“…In this final section, we shall first prove Theorem 0.7 and then deduce Theorem 0.5 using Theorem 0.7 and the affine Roitman torsion theorem [25] for the Levine-Weibel Chow group. 5.1.…”

Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 99%

“…Our goal in this subsection is to prove Theorem 0.5. As we explained in Introduction, our approach is to use the vanishing of SK 0 of the given monoid algebra and then use the affine Roitman torsion theorem for the Levine-Weibel Chow group from [25]. Before we give the details, we recall the definition of the Levine-Weibel Chow group from [27] for reader's reference.…”

Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 99%

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Negative 𝐾-theory and Chow group of monoid algebras

Krishna¹,

Sarwar²

2020

𝐾-Theory in Algebra, Analysis And Topology

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We show, for a finitely generated partially cancellative torsion-free commutative monoid M , that K i (R) ∼ = K i (R[M ]) whenever i ≤ −d and R is a quasi-excellent Q-algebra of Krull dimension d ≥ 1. In particular, K i (R[M ]) = 0 for i < −d. This is a generalization of Weibel's K-dimension conjecture to monoid algebras. We show that this generalization fails for X[M ] if X is not an affine scheme. We also show that the Levine-Weibel Chow group of 0-cycles CH LW 0 (k[M ]) vanishes for any finitely generated commutative partially cancellative monoid M if k is an algebraically closed field. 0.1. Weibel's conjecture for monoid algebras. Recall that a famous conjecture of Weibel [36] asserts that if R is a commutative Noetherian ring of Krull dimension d, then K −d (R) ≃ K −d (R[t 1 , · · · , t n ]) and K i (R[t 1 , · · · , t n ]) = 0 for i < −d and n ≥ 0. An affirmative answer to this conjecture was obtained recently by Kerz, Strunk and Tamme [22]. For Noetherian rings containing Q, this was earlier solved by Cortiñas, Haesemeyer, Schlichting and Weibel [3] (see also [10], [23] and [38] for older results in positive characteristics).The main technical tool that goes into the proof of Weibel's conjecture in [22] is a pro-cdhdescent theorem for algebraic K-theory. However, the final step in the proof of the conjecture 2010 Mathematics Subject Classification. Primary 19D50; Secondary 13F15, 14F35.

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Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 83%

“…In this final section, we shall first prove Theorem 0.7 and then deduce Theorem 0.5 using Theorem 0.7 and the affine Roitman torsion theorem [25] for the Levine-Weibel Chow group. 5.1.…”

Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 99%

Section: Sk 0 and The Levine-weibel Chow Groupmentioning

confidence: 99%

See 1 more Smart Citation

Negative 𝐾-theory and Chow group of monoid algebras

Krishna¹,

Sarwar²

2020

𝐾-Theory in Algebra, Analysis And Topology

Self Cite

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“…The strong Bloch-Srinivas conjecture is proven in § 6 using Theorem 1.1, the recent prodescent theorem of Kerz, Strunk and Tamme [23] and some results on the K-theory in positive characteristic from [26]. A question of Kerz-Saito is answered in a special case as an application of our proof of the strong version of the Bloch-Srinivas conjecture.…”

Section: 2mentioning

confidence: 93%

“…The main ingredients for the surjectivity are some results of Kato and Saito [19]. The injectivity is shown using the Roitman torsion theorems of [26] and [28]. Apart from these, we also need to use a technique of Levine [32] to study the relation between the K-theory of a normal projective scheme and its albanese variety.…”

Section: 2mentioning

confidence: 99%