Une généralisation de la loi de transformation pour les résidus

Boyer, Jean-Yves; Hickel, Michel

doi:10.24033/bsmf.2309

Cited by 10 publications

(5 citation statements)

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“…The case when α = 0 is done in [BVY05, Proposition 3.2]. The general case when α ∈ N r is arbitrary, can be similarly proven by transposing the proof of [BH97] on C n to the case of an arbitrary affine variety, using the Bochner-Martinelli integral representation of affine residues from Proposition 2.3.…”

Section: Which Leads To (23)mentioning

confidence: 99%

Bounds for Multivariate Residues and for the Polynomials in the Elimination Theorem

Sombra¹,

Yger²

2021

MMJ

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We present several upper bounds for the height of global residues of rational forms on an affine variety defined over Q. As an application, we deduce upper bounds for the height of the coefficients in the Bergman-Weil trace formula.We also present upper bounds for the degree and the height of the polynomials in the elimination theorem on an affine variety defined over Q. This is an arithmetic analogue of Jelonek's effective elimination theorem, and it plays a crucial role in the proof of our bounds for the height of global residues.

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Section: Which Leads To (23)mentioning

confidence: 99%

Bounds for Multivariate Residues and for the Polynomials in the Elimination Theorem

Sombra¹,

Yger²

2021

MMJ

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“…for point residues described in (Hartshorne, 1966). See also (Baum and Bott, 1972;Boyer and Hickel, 1997;Griffiths and Harris, 1978;Kytmanov, 1988).…”

Section: Transformation Lawmentioning

confidence: 99%

An effective method for computing Grothendieck point residue mappings

Tajima¹,

Nabeshima²

2020

Preprint

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Grothendieck point residue is considered in the context of computational complex analysis. A new effective method is proposed for computing Grothendieck point residues mappings and residues. Basic ideas of our approach are the use of Grothendieck local duality and a transformation law for local cohomology classes. A new tool is devised for efficiency to solve the extended ideal membership problems in local rings. The resulting algorithms are described with an example to illustrate them. An extension of the proposed method to parametric cases is also discussed as an application.

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“…A fundamental tool associated with the role of multidimensional residue calculus in commutative algebra is the classical transformation law, which appears to be, in the algebraic context (see [44], chapter 7), a formulation in a particular setting of H. Wiebe's theorem; the extension to the current setting can be found, for example, in [29]; the more general version we propose here (and which plays an important role in effectivity questions) is due to A. M. Kytmanov [58]; the presentation we give corresponds to [19] and [11], remark 2.3. Theorem 4.6.…”

Section: P M Amentioning

confidence: 99%