Factorial extensions of regular local rings and invariants of finite groups.
Families of reduced zero-dimensional schemes.
A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...
Fermeture intégrale et changement de base
Fiber cones and the integral closure of ideals.
Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.
Fiber products and Morita duality for commutative rings
Fields with Hanselian Valuation Rings.
Finite dimensional rings of quotients.
In this paper we characterize commutative rings with finite dimensional classical ring of quotients. To illustrate the diversity of behavior of these rings we examine the case of local rings and FPF rings. Our results extend earlier work on rings with zero-dimensional rings of quotients.
Finitely generated Ext algebras.
Flache T1-Stabilität in der Stratifizierung Verseller Entfaltungen.
Flatness testing over singular bases
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
Fonctions -lipschitziennes sur un anneau local et polynômes à valeurs entières
Formes quadratiques sur les anneaux semi-locaux réguliers
Free minimal resolutions and the Betti numbers of the suspension of an -gon.
Frobenius et cohomologie locale