Some Results About Holonomic -Modules
Jan-Erik Björk (1983)
Recherche Coopérative sur Programme n°25
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Jan-Erik Björk (1983)
Recherche Coopérative sur Programme n°25
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Henning Haahr Andersen, Volodymyr Mazorchuk (2015)
Journal of the European Mathematical Society
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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
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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 .
Libor Křižka, Petr Somberg (2015)
Archivum Mathematicum
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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 .
Reza Sazeedeh, Rasul Rasuli (2016)
Colloquium Mathematicae
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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
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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
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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
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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
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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
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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...
Y. Talebi, R. Mohammadi (2016)
Commentationes Mathematicae Universitatis Carolinae
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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...
Pierre Berthelot (2012)
Bulletin de la Société Mathématique de France
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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...
S. O. Smalø, A. Valenta (2007)
Colloquium Mathematicae
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Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration such that for all t. Given a module M with square-free top and a projective cover P, she showed that if and only if M has no proper degeneration where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from...
Otmar Venjakob (2002)
Journal of the European Mathematical Society
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This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, of a -adic analytic group . For without any -torsion element we prove that is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null -module. This is classical when for some integer , but was previously unknown in the non-commutative case. Then the category...
David Hernandez, Bernard Leclerc (2016)
Journal of the European Mathematical Society
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We describe a cluster algebra algorithm for calculating -characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra . This yields a geometric -character formula for tensor products of Kirillov–Reshetikhin modules. When is of type , this formula extends Nakajima’s formula for -characters of standard modules in terms of homology of graded quiver varieties.
Zhanmin Zhu (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be two non-negative integers. A left -module is called -injective, if for every -presented left -module . A right -module is called -flat, if for every -presented left -module . A left -module is called weakly --injective, if for every -presented left -module . A right -module is called weakly -flat, if for every -presented left -module . In this paper, we give some characterizations and properties of -injective modules and -flat modules in...
Frans Loonstra (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si considerano le estensioni chiuse di un -modulo mediante un -modulo nel caso in cui sia un anello semi-artiniano, cioè un anello con la proprietà che per ogni quoziente sia soc . Tali estensioni sono caratterizzate dal fatto che deve essere un sottomodulo semi-puro di .
Ali Fathi (2022)
Czechoslovak Mathematical Journal
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Let be an ideal of a commutative Noetherian ring and be a nonnegative integer. Let and be two finitely generated -modules. In certain cases, we give some bounds under inclusion for the annihilators of and in terms of minimal primary decomposition of the zero submodule of , which are independent of the choice of minimal primary decomposition. Then, by using those bounds, we compute the annihilators of local cohomology and Ext modules in certain cases.