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Solution d'une conjecture de C. Berenstein - A. Yger et invariants de contact à l'infini

Michel Hickel (2001)

Annales de l’institut Fourier

Soient k un corps commutatif et I = ( p 1 , , p m ) k n [ X ] un idéal de l’anneau des polynômes k [ X 1 , , X n ] (éventuellement I = k n [ X ] ). Nous prouvons une conjecture de C. Berenstein - A. Yger qui affirme que pour tout polynôme p , élément de la clôture intégrale I ¯ de l’idéal I , on a une représentation p m = 1 i m p i q i , avec max deg ( q i p i ) m deg p + m d 1 d m , d i = deg p i , 1 i m .

Some results on top local cohomology modules with respect to a pair of ideals

Saeed Jahandoust, Reza Naghipour (2020)

Mathematica Bohemica

Let I and J be ideals of a Noetherian local ring ( R , 𝔪 ) and let M be a nonzero finitely generated R -module. We study the relation between the vanishing of H I , J dim M ( M ) and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian R -module M / J M is equal to its integral closure relative to the Artinian R -module H I , J dim M ( M ) .

Submersions and effective descent of étale morphisms

David Rydh (2010)

Bulletin de la Société Mathématique de France

Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination...

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