Racines approchées, suites génératrices, suffisance des jets
Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero
Let be a field of characteristic zero and G be a finite group of automorphisms of projective plane over . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field is algebraically closed. In this paper we prove that is rational for an arbitrary field of characteristic zero.
Real commutative algebra (I). Places.
Recent progress on Hilbert's Fourteenth Problem via triangular derivations
We give an overview of recent results concerning kernels of triangular derivations of polynomial rings. In particular, we examine the question of finite generation in dimensions 4, 5, 6, and 7.
Recognizing dualizing complexes
Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.
Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings
Reductive group actions on affine varieties and their doubling
We study -actions of the form , where is the dual (to ) -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action is given. It is shown that the doubled actions have a number of nice properties, if is spherical or of complexity one.
Rees algebras on smooth schemes: integral closure and higher differential operator.
Regularity and intersections of bracket powers
Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence. Connections are made with Ohm-Rush content theory, intersection-flatness of the Frobenius map, and various flatness criteria.
Regularity of Ideals and their Radicals.
Relative multiplication and distributive modules
We study the construction of new multiplication modules relative to a torsion theory . As a consequence, -finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.
Remarks and corrections to the paper "Principal ideal theorems for holomorphy rings in fields".
Remarks on Blowing-Up Divisorial Ideals.
Remarks on the Composite G-valuations and their Hypermetric Properties
Remarques sur les idéaux de polynômes et de formes différentielles extérieures I
Remarques sur les idéaux de polynômes et de formes différentielles extérieures II
Residual submodules of multiplication modules.
Resolutions by mapping cones.
Rings all of whose additive endomorphisms are left multiplications.
Rings of global sections in two-dimensional schemes.