Technique de descente et théorèmes d'existence en géométrie algébriques. II. Le théorème d'existence en théorie formelle des modules
Tertiary decomposition in Grothendieck categories
The adcending chain condition for real ideas.
The Artin algebras associated with differential operators on singular affine curves.
The Artin conjecture for Q-algebras.
We give a simplification, in the case of Q-algebras, of the proof of Artin's Conjecture, which says that a regular morphism between Noetherian rings is the inductive limit of smooth morphisms of finite type.
The Category of Graded Modules.
The Construction of a Module of Finite Projective Dimension from a Finitely Generated Module of Finite Injective Dimension.
The covering of rings by valuation rings
The effect on associated prime ideals produced by an extension of the base field.
The Euler Characteristic of a Finitely Generated Module of Finite Injective Dimension.
The finite free extension of artinian -algebras with the strong Lefschetz property
The Heigth of Ideals and Regular Sequences.
The Krull-Schmidt theorem for categories of finitely generated modules over valuation domains.
The lattice of radical filters of a commutative Noetherian ring
The moduli space of commutative algebras of finite rank
The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension calculations...
The order of algebras with nontrivial fixed point subalgebras.
The Picard group of a scheme over an Artin ring
The reduction number of an algebra
The structure of an almost artinian module.
Topological rings that generalize artinian rings.