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:
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...
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 .
H. Marcinkowska
Similarity:
ContentsIntroduction.............................................................................................................................31. Definitions, notations and some auxiliary lemmas...................................................42. The definition of the spaces ..........................................................73. Some properties of the spaces ...................................................104. Some examples of the spaces ....................................................155....
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...
Kari Astala, Daniel Faraco, László Székelyhidi Jr. (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
This paper deals with the theory of linear elliptic partial differential equations with bounded measurable coefficients. We construct in two dimensions examples of weak and so-called very weak solutions, with critical integrability properties, both to isotropic equations and to equations in non-divergence form. These examples show that the general theory, developed in [1, 24] and [2], cannot be extended under any restriction on the essential range of the coefficients. Our constructions...
El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf (2012)
Applicationes Mathematicae
Similarity:
We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem in Ω, where Ω is a bounded open domain of , N ≥ 2 and is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to .
Emmanuel P. Smyrnelis (2010)
Annales Polonici Mathematici
Similarity:
The study of the equation (L₂L₁)*h = 0 or of the equivalent system L*₂h₂ = -h₁, L*₁h₁ = 0, where is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions (u₁,u₂) of the system L₁u₁ = -u₂, L₂u₂ = 0, being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.
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.
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 .
Kamal Paykan (2017)
Czechoslovak Mathematical Journal
Similarity:
A ring is called a right -ring if its socle, , is projective. Nicholson and Watters have shown that if is a right -ring, then so are the polynomial ring and power series ring . In this paper, it is proved that, under suitable conditions, if has a (flat) projective socle, then so does the skew inverse power series ring and the skew polynomial ring , where is an associative ring equipped with an automorphism and an -derivation . Our results extend and unify many existing...
Qin Li, Zuodong Yang (2015)
Annales Polonici Mathematici
Similarity:
By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ in Ω, ⎪ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary or . A nonexistence result is obtained for radially symmetric solutions.
Abdelhafed Elkhadiri (2011)
Annales Polonici Mathematici
Similarity:
Let R be a real closed field, and denote by the ring of germs, at the origin of Rⁿ, of functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring with some natural properties. We prove that, for each n ∈ ℕ, is a noetherian ring and if R = ℝ (the field of real numbers), then , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring . ...
E. Shargorodsky
Similarity:
Let M be a -smooth n-dimensional manifold and ν₁, ..., νₙ be -smooth vector fields on M which span the tangent space at each point x ∈ M. The vector fields ν₁, ..., νₙ may have nonzero commutators. We construct a calculus of pseudodifferential operators (ψDOs) which act on sections of vector bundles over M and have symbols belonging to anisotropic analogues of the Hörmander classes , and apply it to semi-elliptic operators generated by ν₁,...,νₙ. The results obtained include the...
Daniel Marahrens, Felix Otto (2015)
Mathematica Bohemica
Similarity:
We consider a random, uniformly elliptic coefficient field on the lattice . The distribution of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green’s function satisfy optimal annealed estimates which are and , respectively, in probability, i.e., they obtained bounds on and . In particular, the elliptic Green’s function satisfies optimal annealed bounds. In their recent work,...
Honghui Yin, Zuodong Yang (2011)
Annales Polonici Mathematici
Similarity:
Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems ⎧ , x ∈ Ω, ⎨ , x ∈ Ω, ⎩ u = v = 0, x∈ ∂Ω, where 1 < q < p < N and is an open bounded smooth domain. Here λ₁, λ₂, μ ≥ 0 and (i = 1,2) are sign-changing functions, where , , and denotes the p-Laplace operator. We use variational methods.
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...
A. El Khalil, S. El Manouni, M. Ouanan (2009)
Applicationes Mathematicae
Similarity:
Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem ⎧ in ⎨ ⎩ u > 0, , where 1 < p < N; a(x) is assumed to satisfy a coercivity condition; h(x) and g(x) are not necessarily bounded but satisfy some integrability restrictions.
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...
Lin Wei, Zuodong Yang (2010)
Annales Polonici Mathematici
Similarity:
We study the existence of positive solutions to ⎧ on Ω, ⎨ ⎩ u = 0 on ∂Ω, where Ω is or an unbounded domain, q(x) is locally Hölder continuous on Ω and p > 1, γ > -(p-1).
Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)
Czechoslovak Mathematical Journal
Similarity:
Let be a graded ring and be an integer. We introduce and study the notions of Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules by using the notion of special finitely presented graded modules. On -gr-coherent rings, we investigate the relationships between Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules. Among other results, we prove that any graded module in -gr (or gr-) admits a Gorenstein -FP-gr-injective (or Gorenstein -gr-flat) cover and preenvelope,...
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...