On triviality of the Euler class group of a deleted neighbourhood of a smooth local scheme

Das, Mrinal Kanti

doi:10.1090/s0002-9947-2012-05591-7

Cited by 7 publications

(5 citation statements)

References 30 publications

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“…In this subsection, we establish Theorem A.1.4 which improves those results. To this end, we begin by recalling the following improvement of [12,Theorem 3.8] from [18]. We now prove the following result; the idea of this proof is similar to that of [12,Lemma 4.3,Remark 4.6].…”

Section: A1 Homotopy Invariance Of Euler Class Groupsmentioning

confidence: 89%

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Euler class groups and motivic stable cohomotopy (with an appendix by Mrinal Kanti Das)

Asok

Fasel

2021

J. Eur. Math. Soc.

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We study maps from a smooth scheme to a motivic sphere in the Morel-Voevodsky A 1 -homotopy category, i.e., motivic cohomotopy sets. Following Borsuk, we show that, in the presence of suitable hypotheses on the dimension of the source, motivic cohomotopy sets can be equipped with functorial abelian group structures. We then explore links between motivic cohomotopy groups, Euler class groups à la Nori-Bhatwadekar-Sridharan and Chow-Witt groups. We show that, again under suitable hypotheses on the base field k, if X is a smooth affine k-variety of dimension d , then the Euler class group of codimension d cycles coincides with the codimension d Chow-Witt group; the identification proceeds by comparing both groups with a suitable motivic cohomotopy group. As a byproduct, we describe the Chow group of zero cycles on a smooth affine k-scheme as the quotient of the free abelian group on zero cycles by the subgroup generated by reduced complete intersection ideals; this answers a question of S. Bhatwadekar and R. Sridharan.

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Section: A1 Homotopy Invariance Of Euler Class Groupsmentioning

confidence: 89%

“…[18, Theorem 4.12]). Let R be a regular ring of dimension d which has essentially finite type over a field k and infinite residue fields.…”

mentioning

confidence: 99%

Euler class groups and motivic stable cohomotopy (with an appendix by Mrinal Kanti Das)

Asok

Fasel

2021

J. Eur. Math. Soc.

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“…induced from Φ. Since I ′ (0) = A and P has a unimodular element, ψ can be lifted to a surjection [2, 4.13] and [8], ψ 1 can be lifted to a surjection Ψ :…”

Section: Main Theoremmentioning

confidence: 99%

“…The best result that we have so far is the one due to Bhatwadekar-Keshari [2, 4.13] where they assume A to be a regular domain of dimension d which is essentially of finite type over an infinite perfect field k and further that ht I = n with 2n ≥ d + 3. It has been shown in [8] that one need not take the field to be perfect in [2, 4.13].…”

Section: Introductionmentioning

confidence: 99%

A question of Nori, Segre classes of ideals and other applications

Das

Keshari

2014

Preprint

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“…By (2.9), for all n ≫ 0, Proof. When A is a k-spot, then P = A n and the result is proved in [6,Theorem 4.2]. In the general case, let Σ be the set of all s ∈ A such that φ s lifts to a surjection Ψ : P s [T ] ։ I s .…”

Section: Introductionmentioning

confidence: 99%