Zero-cycle groups on algebraic varieties

Binda, Federico; Krishna, Amalendu

doi:10.5802/jep.183

Cited by 6 publications

(18 citation statements)

References 37 publications

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“…1 If one wants to replace Λ by Z, then one should replace seminormal by weakly normal. 2 This assumption is very hard to check even if it is unavoidable in [7].…”

Section: 25mentioning

confidence: 99%

“…0 (X) by Lemma 4.9. If (C, f ) if of type (2) in the definition of CH EKW 0 (X) in § 4.4, then C ⊂ X is a Cartier curve (see § 3.2) by [7,Lem. 7.6] and hence, div(f ) already dies in CH LW 0 (X).…”

Section: Motivic Cohomology Of Normal Crossing Schemesmentioning

confidence: 99%

“…The case (3) of Theorem 1.1 is known by [7,Thm. 1.1] (we included it in the theorem only for completeness).…”

Section: Introductionmentioning

confidence: 99%

“…We expect the condition d ≤ 2 in (2) to be unnecessary, but do not know how to show it. However, the condition on char(k) in (3) and algebraicity of k over Q in (4) can not be relaxed (see [7,Thm. 4.4]).…”

Section: Introductionmentioning

confidence: 99%

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Suslin homology via cycles with modulus and applications

Binda¹,

Krishna²

2022

Preprint

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We show that for a smooth projective variety X over a field k and a reduced effective Cartier divisor D ⊂ X, the Chow group of 0-cycles with modulus CH 0 (X D) coincides with the Suslin homology H S 0 (X ∖ D) under some necessary conditions on k and D. Several consequences are derived. Contents 1. Introduction 1 2. Algebraic and homotopy K-groups of a double 6 3. Proof of the main result 13 4. Motivic cohomology of normal crossing schemes 19 5. Question of Barbieri-Viale and Kahn 24 References 25

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“…1 If one wants to replace Λ by Z, then one should replace seminormal by weakly normal. 2 This assumption is very hard to check even if it is unavoidable in [7].…”

Section: 25mentioning

confidence: 99%

Section: Motivic Cohomology Of Normal Crossing Schemesmentioning

confidence: 99%

“…The case (3) of Theorem 1.1 is known by [7,Thm. 1.1] (we included it in the theorem only for completeness).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Suslin homology via cycles with modulus and applications

Binda¹,

Krishna²

2022

Preprint

Self Cite

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show abstract

“…This map is clearly an isomorphism if d ≤ 1. However, it is known (see [7,Thm. 1.1]) that φ X|D may not be an isomorphism if d ≥ 2 (even if k is algebraically closed).…”

Section: Introductionmentioning

confidence: 99%

Suslin homology via cycles with modulus and applications

Binda

Krishna

2022

Trans. Amer. Math. Soc.

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We show that for a smooth projective variety X X over a field k k and a reduced effective Cartier divisor D ⊂ X D \subset X , the Chow group of 0-cycles with modulus C H 0 ( X | D ) CH_0(X|D) coincides with the Suslin homology H 0 S ( X ∖ D ) H^S_0(X \setminus D) under some necessary conditions on k k and D D . We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.

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Zero-cycles in families of rationally connected varieties

Lüders

2024

Sel. Math. New Ser.

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We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally connected. We further extend this result to certain higher Chow groups and develop conjectures in the non-smooth case. Our main results generalise a result of Kollár (Publ. Res. Inst. Math. Sci. 40(3):689–708, 2004).

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Zero-cycle groups on algebraic varieties

Cited by 6 publications

References 37 publications

Suslin homology via cycles with modulus and applications

Suslin homology via cycles with modulus and applications

Suslin homology via cycles with modulus and applications

Zero-cycles in families of rationally connected varieties

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