scholarly journals Cohen–Macaulay Modules and Holonomic Modules Over Filtered Rings

2009 ◽  
Vol 37 (2) ◽  
pp. 406-430
Author(s):  
Hiroki Miyahara ◽  
Kenji Nishida
Keyword(s):  
Holonomic Modules

scholarly journals Holonomic modules for rings of invariant differential operators

2021 ◽  
pp. 1-18
Author(s):  
Vyacheslav Futorny ◽  
João Schwarz
Keyword(s):  
Differential Operators ◽  
Main Tool ◽  
Bernstein Inequality ◽  
Invariant Differential Operators ◽  
Weyl Algebras ◽  
Invariant Differential ◽  
Quotient Varieties ◽  
Generalized Weyl Algebras ◽  
A Finite Group ◽  
Holonomic Modules

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals [Formula: see text].

scholarly journals A Bernstein-Gabber-Joseph theorem for affine algebras

1999 ◽  
Vol 42 (2) ◽  
pp. 311-332 ◽  
Author(s):  
V. V. Bavula ◽  
T. H. Lenagan
Keyword(s):  
Weyl Algebra ◽  
Simple Algebra ◽  
Famous Result ◽  
Affine Algebras ◽  
Carry Over ◽  
Definition Of ◽  
Holonomic Modules

Bernstein's famous result, that any non-zero module M over the n-th Weyl algebra An satisfies GKdim(M)≥GKdim(An)/2, does not carry over to arbitrary simple affine algebras, as is shown by an example of McConnell. Bavula introduced the notion of filter dimension of simple algebra to explain this failure. Here, we introduce the faithful dimension of a module, a variant of the filter dimension, to investigate this phenomenon further and to study a revised definition of holonomic modules. We compute the faithful dimension for certain modules over a variant of the McConnell example to illustrate the utility of this new dimension.

On Some Topological Properties of Fourier Transforms of Regular Holonomic -Modules

2020 ◽  
Vol 63 (2) ◽  
pp. 454-468
Author(s):  
Yohei Ito ◽  
Kiyoshi Takeuchi
Keyword(s):  
Fourier Transforms ◽  
Classical Theorem ◽  
Topological Properties ◽  
Holonomic Modules

AbstractWe study Fourier transforms of regular holonomic ${\mathcal{D}}$-modules. In particular, we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic ${\mathcal{D}}$-modules will be given. Moreover, we give a new proof of the classical theorem of Brylinski and improve it by showing its converse.

scholarly journals RIEMANN–HILBERT CORRESPONDENCE FOR MIXED TWISTOR -MODULES

2017 ◽  
Vol 18 (3) ◽  
pp. 629-672 ◽  
Author(s):  
Teresa Monteiro Fernandes ◽  
Claude Sabbah
Keyword(s):  
Derived Category ◽  
Inverse Property ◽  
Holonomic Modules

We introduce the notion of regularity for a relative holonomic ${\mathcal{D}}$-module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961–4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative ${\mathcal{D}}$-modules underlying a regular mixed twistor ${\mathcal{D}}$-module, this functor satisfies the left quasi-inverse property.

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