Groupes de Chow-Witt

Fasel, Jean

doi:10.24033/msmf.425

Cited by 73 publications

(117 citation statements)

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“…Therefore The case d = 2 is a little bit different and was known from [5] or [13]. As a straightforward consequence of our results, we get the following theorem: …”

Section: Chow-witt Groupsmentioning

confidence: 66%

“…The implicationc d (P ) = 0 ⇒ P Q ⊕ A follows then from Propositions 23 and 24. The other implication is Corollary 13.3.3 in [13].…”

Section: Let {E(n)mentioning

confidence: 91%

“…The graduation on the above complex is such that x p ∈X (p) G n−p (k(x p ), ω L x p ) sits in degree p. The following definition is due to Barge and Morel ([5], see also [13]):…”

Section: Identification Of Some Differentialsmentioning

confidence: 99%

“…In order to make this identification explicit, we briefly recall the definition of the Chow-Witt groups of a regular scheme in Section 4.1. The reference for that section is [13]. Finally, we put everything together to prove Morel's theorem in dimension 3 (Theorem 38).…”

Section: Introductionmentioning

confidence: 99%

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Chow–Witt groups and Grothendieck–Witt groups of regular schemes

Fasel

Srinivas²

2009

Advances in Mathematics

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Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective Amodule of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d 3, we show that the vanishing of its Euler class in the corresponding Grothendieck-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. If d is odd, we also get some results in that direction. If A is regular, we show that the Chow-Witt groups defined by Morel and Barge appear naturally as some homology groups of a Gersten-type complex in Grothendieck-Witt theory. From this, we deduce that if d = 3 then the vanishing of the Euler class of P in the corresponding Chow-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. Crown

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“…Therefore The case d = 2 is a little bit different and was known from [5] or [13]. As a straightforward consequence of our results, we get the following theorem: …”

Section: Chow-witt Groupsmentioning

confidence: 66%

“…The implicationc d (P ) = 0 ⇒ P Q ⊕ A follows then from Propositions 23 and 24. The other implication is Corollary 13.3.3 in [13].…”

Section: Let {E(n)mentioning

confidence: 91%

“…The graduation on the above complex is such that x p ∈X (p) G n−p (k(x p ), ω L x p ) sits in degree p. The following definition is due to Barge and Morel ([5], see also [13]):…”

Section: Identification Of Some Differentialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chow–Witt groups and Grothendieck–Witt groups of regular schemes

Fasel

Srinivas²

2009

Advances in Mathematics

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“…While we have particular interest in the setting of singular varieties and we also provide further insight into nonsingular varieties in these articles. Our interest in Witt theory stems from the introduction of Chow-Witt groups, [1] and developed by Fasel [3], as obstruction groups for projective modules to split off a free direct summand. The readers are referred to [4] for further introductory comments.…”

Section: Introductionmentioning

confidence: 99%

Stability of locally CMFPD homologies under duality

Mandal

Sane

2015

Journal of Algebra

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Homotopy Invariance of the Sheaf W Nis and of Its Cohomology

Panin

2010

Quadratic Forms, Linear Algebraic Groups, and Cohomology

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A conjecture of F.Morel states that the motivic group π 0,0 (k) of a perfect field k coincides with the Grothendieck-Witt group GW (k) of quadratic forms over k provided that char(k) = 2. Morel's proof of the conjecture requires the the following result: the Nisnevich sheaf W N is associated with the presheaf X → W (X) is homotopy invariant and all its Nisnevich cohomology are homotopy invariant too. A rather short and self-contained proof of the result is given here. Another proof is due to J.Hornbostel [H].

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Groupes de Chow-Witt

Cited by 73 publications

References 0 publications

Chow–Witt groups and Grothendieck–Witt groups of regular schemes

Chow–Witt groups and Grothendieck–Witt groups of regular schemes

Stability of locally CMFPD homologies under duality

Homotopy Invariance of the Sheaf W Nis and of Its Cohomology

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