scholarly journals On the Jacobian ideal of the module of differentials

1969 ◽  
Vol 21 (2) ◽  
pp. 422-422 ◽  
Author(s):  
Joseph Lipman
Keyword(s):  
Jacobian Ideal ◽  
Module Of Differentials

scholarly journals On algebra with universal finite module of differentials

1981 ◽  
Vol 83 ◽  
pp. 107-121 ◽  
Author(s):  
Norio Yamauchi
Keyword(s):  
Local Ring ◽  
Positive Characteristic ◽  
Regularity Theorem ◽  
Local Case ◽  
Finite Module ◽  
Characteristic Case ◽  
Differential Modules ◽  
Module Of Differentials

Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.

scholarly journals On the module of differentials of order n of hypersurfaces

2020 ◽  
Vol 224 (2) ◽  
pp. 536-550 ◽  
Author(s):  
Paul Barajas ◽  
Daniel Duarte
Keyword(s):  
Module Of Differentials

A note on normality and the module of differentials

1968 ◽  
Vol 105 (4) ◽  
pp. 291-293 ◽  
Author(s):  
Wolmer V. Vasconcelos
Keyword(s):  
Module Of Differentials

scholarly journals On Plane Curves with Double and Triple Points

2016 ◽  
Vol 119 (1) ◽  
pp. 60 ◽  
Author(s):  
Nancy Abdallah
Keyword(s):  
Plane Curve ◽  
Plane Curves ◽  
Jacobian Ideal ◽  
Pole Order ◽  
Hodge Filtration ◽  
Triple Points

We describe in simple geometric terms the Hodge filtration on the cohomology $H^*(U)$ of the complement $U=\mathsf{P}^2 \setminus C$ of a plane curve $C$ with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration on $H^2(U)$ are given.

scholarly journals The different and differentials of local fields with imperfect residue fields

1997 ◽  
Vol 40 (2) ◽  
pp. 353-365 ◽  
Author(s):  
Bart de Smit
Keyword(s):  
Galois Extension ◽  
Correction Term ◽  
Residue Field ◽  
Field Extension ◽  
Local Fields ◽  
Valuation Rings ◽  
Complete Field ◽  
Residue Fields ◽  
Residue Characteristic ◽  
Module Of Differentials

Let K be a complete field with respect to a discrete valuation and let L be a finite Galois extension of K. If the residue field extension is separable then the different of L/K can be expressed in terms of the ramification groups by a well-known formula of Hilbert. We will identify the necessary correction term in the general case, and we give inequalities for ramification groups of subextensions L′/K in terms of those of L/K. A question of Krasner in this context is settled with a counterexample. These ramification phenomena can be related to the structure of the module of differentials of the extension of valuation rings. For the case that [L: K] = p2, where p is the residue characteristic, this module is shown to determine the correction term in Hilbert's formula.

scholarly journals Orbifolding Frobenius Algebras

2003 ◽  
Vol 14 (06) ◽  
pp. 573-617 ◽  
Author(s):  
Ralph M. Kaufmann
Keyword(s):  
General Theory ◽  
Gauge Group ◽  
Physical Theory ◽  
Group Actions ◽  
Vector Spaces ◽  
Algebraic Structures ◽  
Jacobian Ideal ◽  
Frobenius Algebras

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e. orbifold theories. In this context, we introduce and axiomatize these algebras. Furthermore, we define geometric cobordism categories whose functors to the category of vector spaces are parameterized by these algebras. The theory is also extended to the graded and super-graded cases. As an application, we consider Frobenius algebras having some additional properties making them more tractable. These properties are present in Frobenius algebras arising as quotients of Jacobian ideal, such as those having their origin in quasi-homogeneous singularities and their symmetries.

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