Some Results About Holonomic -Modules
Jan-Erik Björk (1983)
Recherche Coopérative sur Programme n°25
Similarity:
Jan-Erik Björk (1983)
Recherche Coopérative sur Programme n°25
Similarity:
Henning Haahr Andersen, Volodymyr Mazorchuk (2015)
Journal of the European Mathematical Society
Similarity:
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for and for finite dimensional -modules we are able...
Tong Liu (2013)
Journal de Théorie des Nombres de Bordeaux
Similarity:
Let be a finite extension over and the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over .
Rongmin Zhu, Jiaqun Wei (2023)
Czechoslovak Mathematical Journal
Similarity:
Let be a dg--module, the endomorphism dg-algebra of . We know that if is a good silting object, then there exist a dg-algebra and a recollement among the derived categories of , of and of . We investigate the condition under which the induced dg-algebra is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained....
Libor Křižka, Petr Somberg (2015)
Archivum Mathematicum
Similarity:
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
Maryam Salimi (2019)
Czechoslovak Mathematical Journal
Similarity:
Let be a commutative Noetherian ring, and let be a semidualizing -module. The notion of -tilting -modules is introduced as the relative setting of the notion of tilting -modules with respect to . Some properties of tilting and -tilting modules and the relations between them are mentioned. It is shown that every finitely generated -tilting -module is -projective. Finally, we investigate some kernel subcategories related to -tilting modules.
Reza Sazeedeh, Rasul Rasuli (2016)
Colloquium Mathematicae
Similarity:
Let R be a commutative noetherian ring, let be an ideal of R, and let be a subcategory of the category of R-modules. The condition , defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to belong to . In this paper, we define and study the class consisting of all modules satisfying . If and are ideals of R, we get a necessary and sufficient condition for to satisfy and simultaneously. We also...
Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
An -module has an almost trivial dual if there are no epimorphisms from to the free -module of countable infinite rank . For every natural number , we construct arbitrarily large separable -free -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.
Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)
Journal of the European Mathematical Society
Similarity:
It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...
Paul Balmer (2013)
Journal of the European Mathematical Society
Similarity:
Let be a field of characteristic . Let be a finite group of order divisible by and a -Sylow subgroup of . We describe the kernel of the restriction homomorphism , for the group of endotrivial representations. Our description involves functions that we call weak -homomorphisms. These are generalizations to possibly non-normal of the classical homomorphisms appearing in the normal case.
João Pedro P. dos Santos (2011)
Bulletin de la Société Mathématique de France
Similarity:
We study liftings or deformations of -modules ( is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given -module in positive characteristic. At the end we compare...
Piotr Dowbor, Andrzej Mróz (2008)
Colloquium Mathematicae
Similarity:
Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector such that is studied. A precise formula for , for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors...
Kamal Bahmanpour (2022)
Czechoslovak Mathematical Journal
Similarity:
Let be an ideal of a commutative Noetherian ring . It is shown that the -modules are -cofinite for all finitely generated -modules and all if and only if the -modules and are -cofinite for all finitely generated -modules , and all integers .
Y. Talebi, R. Mohammadi (2016)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
In this paper we introduce the concept of -extending modules by -rational submodules and study some properties of such modules. It is shown that the set of all -rational left ideals of is a Gabriel filter. An -module is called -extending if every submodule of is -rational in a direct summand of . It is proved that is -extending if and only if , such that is a -extending submodule of . An example is given to show that the direct sum of -extending modules need not...
Engin Kaynar, Burcu N. Türkmen, Ergül Türkmen (2019)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
A left module over an arbitrary ring is called an -module (or an -module) if every submodule of with is a direct summand of (a supplement in, respectively) . In this paper, we investigate the various properties of -modules and -modules. We prove that is an -module if and only if , where is semisimple. We show that a finitely generated -module is semisimple. This gives us the characterization of semisimple rings in terms of -modules. We completely determine the structure...
Pierre Berthelot (2012)
Bulletin de la Société Mathématique de France
Similarity:
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it...
Chao Wang, Xiao Yan Yang (2017)
Czechoslovak Mathematical Journal
Similarity:
Let be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective -modules under the condition that is a cocompatible -bimodule, we establish a recollement of the stable category . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over .