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La conjecture de Green générique

Arnaud Beauville (2003/2004)

Séminaire Bourbaki

Une courbe C projective et lisse de genre g , non hyperelliptique, admet un plongement canonique dans un espace projectif ℙ g - 1 . Un résultat classique affirme que l’idéal gradué I C des équations de C dans ℙ g - 1 est engendré par ses éléments de degré 2 , sauf si C admet certains systèmes linéaires très particuliers. Mark Green en a proposé il y a vingt ans une vaste généralisation, qui décrit la résolution minimale de I C en fonction de l’existence de systèmes linéaires spéciaux sur C . Claire Voisin vient de...

Lie description of higher obstructions to deforming submanifolds

Marco Manetti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

To every morphism χ : L → M of differential graded Lie algebras we associate a functors of artin rings Def χ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ . Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map.

Lifting D -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

We study liftings or deformations of D -modules ( D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic D -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given D -module in positive characteristic. At the end we compare the problems...

Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour (2022)

Czechoslovak Mathematical Journal

Let I be an ideal of a commutative Noetherian ring R . It is shown that the R -modules H I j ( M ) are I -cofinite for all finitely generated R -modules M and all j ∈ ℕ 0 if and only if the R -modules Ext R i ( N , H I j ( M ) ) and Tor i R ( N , H I j ( M ) ) are I -cofinite for all finitely generated R -modules M , N and all integers i , j ∈ ℕ 0 .

Local-global principle for annihilation of general local cohomology

J. Asadollahi, K. Khashyarmanesh, Sh. Salarian (2001)

Colloquium Mathematicae

Let A be a Noetherian ring, let M be a finitely generated A-module and let Φ be a system of ideals of A. We prove that, for any ideal in Φ, if, for every prime ideal of A, there exists an integer k(), depending on , such that k ( ) kills the general local cohomology module H Φ j ( M ) for every integer j less than a fixed integer n, where Φ : = : ∈ Φ , then there exists an integer k such that k H Φ j ( M ) = 0 for every j < n.

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