-theory, -rings, and formal groups
-torsionless modules with finite Gorenstein dimension
Let be a commutative Noetherian ring. It is shown that the finitely generated -module with finite Gorenstein dimension is reflexive if and only if is reflexive for with , and for with . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for we give a characterization of -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...
Kaplansky classes
Klassen von Moduln über Dedekind-Ringen und Satz von Stein-Serre
Koszul complexes with isomorphic homology.
Koszul homology and Lie algebras with application to generic forms and points.
K-Theory and Analytic Isomorphisms.
La conjecture de Green générique
Une courbe projective et lisse de genre , non hyperelliptique, admet un plongement canonique dans un espace projectif . Un résultat classique affirme que l’idéal gradué des équations de dans est engendré par ses éléments de degré , sauf si 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 en fonction de l’existence de systèmes linéaires spéciaux sur . Claire Voisin vient de...
La filtration de Gabriel
Large homomorphisms of local rings.
Le caractère additif des déviations des anneaux locaux.
Le groupe des classes de l'algèbre affine d'une forme quadratique
Lech-Hironaka Inequalities for Flat couples of local rings.
Length Formulas for the Local Cohomology of Exterior Powers.
Les modules projectifs de type fini sur un anneau de polynômes sur un corps sont libres
Libération des modules projectifs sur certains anneaux de polynômes
Lie description of higher obstructions to deforming submanifolds
To every morphism of differential graded Lie algebras we associate a functors of artin rings whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of . 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 -modules from positive to zero characteristic
We study liftings or deformations of -modules ( 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 -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 -module in positive characteristic. At the end we compare the problems...
Linear forms on modules of projective dimension one.
Linear systems with multiple base points in .