共查询到20条相似文献,搜索用时 15 毫秒
1.
Umberto Zannier 《Archiv der Mathematik》1997,68(2):129-138
Let/e fєℤ[x, y] be an absolutely irreducible polynomial. A classical result by Ostrowski states that the reduction modulo p of f remains absolutely irreducible for all large prime numbers p. Here we give a new sufficient condition on p for the conclusion to hold. The result, which holds for polynomials defined over arbitrary discrete valuation rings, also
implies equality of the genera of the curves defined by f and its reduction. The method of proof stems from Hensel’s principle and analytic continuation of p-adic analytic functions, following Dwork and Robba. 相似文献
2.
Aldo J. Lazar 《Israel Journal of Mathematics》2010,179(1):145-155
We prove that if X is a locally compact σ-compact space, then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if
X is second countable locally compact, then γ(X) is second countable locally compact Hausdorff if and only if it is first countable. The interest in these results originated
in [1] and [7] where the primitive ideal space of a C*-algebra was considered. 相似文献
3.
Jin Yun GUO Bing Jun LI Qiu Xian WU 《数学学报(英文版)》2006,22(3):849-854
In this paper, we prove that there is a natural equivalence between the category F1(x) of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables. 相似文献
4.
Otmar Venjakob 《Journal of the European Mathematical Society》2002,4(3):271-311
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, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion
of a pseudo-nullΛ-module. This is classical when G=ℤ
k
p
for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied
and we obtain a weak structure theorem for the ℤ
p
-torsion part of a finitely generated Λ-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum
equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001 相似文献
5.
L. Oubbi 《Rendiconti del Circolo Matematico di Palermo》2005,54(3):451-462
It is known that every locally A-convex algebra (E, τ) can be endowed with, at least, one locally m-convex topology stronger thanτ. In this note, we answer several questions concerning such locally m-convex topologies. In particular, we show that, unlike
what is asserted in several previous papers, the collection of all such topologies does not have any weakest element in general. 相似文献
6.
Umberto Zannier 《Israel Journal of Mathematics》2001,124(1):93-114
We investigate the existence of distinct polynomialsF, G having roots of prescribed multiplicities and deg(F −G) as small as predicted by Mason’sabc theorem. The case of characteristic zero has been treated completely in a previous paper, but those methods do not apply
in positive characteristic. Here we study this problem through reduction; it turns out that what we require amounts to proving
good reduction for certain covers of the projective line, unramified except above 0, 1, ∞. We shall give sufficient conditions
for good reduction of those covers, which sometimes go beyond known criteria due to Grothendieck, Fulton and Beckmann. The
methods are completely different from those used by such authors and rely on results by Dwork and Robba onp-adic analytic continuation of Puiseux series. 相似文献
7.
A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach,
we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the triplet vertex algebra
W(p){\mathcal{W}(p)} and for other subalgebras of lattice vertex algebras and their N = 1 super extensions. We analyze in detail indecomposable modules obtained in this way, giving further evidence for the conjectural
equivalence between the category of W(p){\mathcal{W}(p)}-modules and the category of modules for the restricted quantum group [`(U)]q(sl2){\overline{\mathcal{U}}_q(sl_2)} , q = e
π
i/p
. We also construct logarithmic representations for a certain affine vertex operator algebra at admissible level realized
in Adamović (J. Pure Appl. Algebra 196:119–134, 2005). In this way we prove the existence of the logarithmic representations
predicted in Gaberdiel (Int. J. Modern Phys. A 18, 4593–4638, 2003). Our approach enlightens related logarithmic intertwining
operators among indecomposable modules, which we also construct in the paper. 相似文献
8.
ChunGilPARK 《数学学报(英文版)》2004,20(6):1047-1056
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
9.
Eberhard Mayerhofer 《Mathematische Nachrichten》2007,280(11):1297-1301
We show that contrary to recent papers by S. Albeverio, A. Yu. Khrennikov and V. Shelkovich, point values do not determine elements of the so‐called p ‐adic Colombeau–Egorov algebra ??(?n p ) uniquely. We further show in a more general way that for an Egorov algebra ??(M, R) of generalized functions on a locally compact ultrametric space (M, d) taking values in a nontrivial ring, a point value characterization holds if and only if (M, d) is discrete. Finally, following an idea due to M. Kunzinger and M. Oberguggenberger, a generalized point value characterization of ??(M, R) is given. Elements of ??(?n p ) are constructed which differ from the p ‐adic δ ‐distribution considered as an element of ??(?n p ), yet coincide on point values with the latter. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Philippe Eyssidieux 《Mathematische Annalen》2000,317(3):527-566
In order to study the group of holomorphic sections of the pull-back to the universal covering space of an holomorphic vector bundle on a compact complex
manifold, it would be convenient to have a cohomological formalism, generalizing Atiyah's index theorem. In [Eys99], such a formalism is proposed in a restricted context. To each coherent analytic sheaf on a n-dimensionnal smooth projective variety and each Galois infinite unramified covering , whose Galois group is denoted by , cohomology groups denoted by are attached, such that:
1. The underly a cohomological functor on the abelian category of coherent analytic sheaves on X.
2. If is locally free, is the group of holomorphic sections of the pull-back to of the holomorphic vector bundle underlying .
3. belongs to a category of -modules on which a dimension function with real values is defined.
4. Atiyah's index theorem holds [Ati76]:
The present work constructs such a formalism in the natural context of complex analytic spaces. Here is a sketch of the main
ideas of this construction, which is a Cartan-Serre version of [Ati76]. A major ingredient will be the construction [Farb96]
of an abelian category containing every closed -submodule of the left regular representation. In topology, this device enables one to use standard sheaf theoretic methods
to study Betti numbers [Ati76] and Novikov-Shubin invariants [NovShu87]. It will play a similar r?le here. We first construct a -cohomology theory () for coherent analytic sheaves on a complex space endowed with a proper action of a group such that conditions 1-2 are fulfilled. The -cohomology on the Galois covering of a coherent analytic sheaf onX is the ordinary cohomology of a sheaf on X obtained by an adequate completion of the tensor product of by the locally constant sheaf on X associated to the left regular representation of the discrete group in the space of functions on . Then, we introduce an homological algebra device, montelian modules, which can be used to calculate the derived category
of and are a good model of the Čech complex calculating -cohomology. Using this we prove that , if X is compact. This is stronger than condition 3, since this also yields Novikov-Shubin type invariants. To explain the title
of the article, Betti numbers and Novikov-Shubin invariants of are the Von Neumann invariants of the coherent analytic sheaf . We also make the connection with Atiyah's -index theorem [Ati76] thanks to a Leray-Serre spectral sequence. From this, condition 4 is easily deduced.
Received: 30 October 1998 / Published online: 8 May 2000 相似文献
Received: 30 October 1998 / Published online: 8 May 2000 相似文献
11.
For a quasi-Hopf algebra H, a left H-comodule algebra and a right H-module coalgebra C we will characterize the category of Doi–Hopf modules C ?(H) in terms of modules. We will also show that for an H-bicomodule algebra and an H-bimodule coalgebra C the category of generalized Yetter–Drinfeld modules (H) C is isomorphic to a certain category of Doi–Hopf modules. Using this isomorphism we will transport the properties from the category of Doi–Hopf modules to the category of generalized Yetter–Drinfeld modules. 相似文献
12.
The unitization of a locally uniformlyA-p-convex algebra is not always of the same type. In non unitary ones, we exhibit a strongerm-p-convex topology, which plays the role of ap-norm in the unitary case. Some structure results are given, while we also supply hints to clarify the aforesaid phenomenon. 相似文献
13.
14.
In this paper, a class of generalized Verma modules M(V) over some Block type Lie algebra ℬ(G) are constructed, which are induced from nontrivial simple modules V over a subalgebra of ℬ(G). The irreducibility of M(V) is determined.
相似文献
15.
Coherent continuation π
2 of a representation π
1 of a semisimple Lie algebra arises by tensoring π
1 with a finite dimensional representation F and projecting it to the eigenspace of a particular infinitesimal character. Some
relations exist between the spaces of harmonic spinors (involving Kostant’s cubic Dirac operator and the usual Dirac operator)
with coefficients in the three modules. For the usual Dirac operator we illustrate with the example of cohomological representations
by using their construction as generalized Enright-Varadarajan modules. In [9] we considered only discrete series, which arises
as generalized Enright-Varadarajan modules in the particular case when the parabolic subalgebra is a Borel subalgebra. 相似文献
16.
The maximal ideal space ΔG of the measure algebra M(G) of a locally compact abelian group G is a compact commutative semitopological semigroup. In this
paper we show that cℓ Ĝ the closure of Ĝ, the dual of G, in ΔG can contain maximal subgroups which are not locally compact. We have previously characterized the locally compact maximal
subgroups of cℓ Ĝ as arising from locally compact topologies on G which are finer than the original topology.
This research was supported in part by NSF contract number GP-19852. 相似文献
17.
18.
Francesco Baldassarri 《Inventiones Mathematicae》2010,182(3):513-584
This paper deals with connections on non-archimedean, especially p-adic, analytic curves, in the sense of Berkovich. The curves must be compact but the connections are allowed to have a finite
number of meromorphic singularities on them. For any choice of a semistable formal model of the curve, we define a geometric, intrinsic notion of normalized radius of convergence of a full set of local solutions as a function on the curve, with values in (0,
1]. For a sufficiently refined choice of the semistable model, we prove continuity, logarithmic concavity and logarithmic
piece-wise linearity of that function. We introduce and characterize Robba connections, that is connections whose sheaf of solutions is constant on any open disk contained in the curve, precisely as it happens
in the classical case. 相似文献
19.
We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction
of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central to the
classical orbit method. Instead, Kirillov’s character formula becomes the fundamental object of study. Our results are then
used to produce an alternate proof of the orbit method classification of complex irreducible representations of p-groups of nilpotence class < p, where p is a prime, and of continuous complex irreducible representations of uniformly powerful pro-p-groups (with a certain modification for p = 2). As a main application, we give a quick and transparent proof of the p-adic analogue of Brown’s theorem, stating that for a nilpotent Lie group over ℚp the Fell topology on the set of isomorphism classes of its irreducible representations coincides with the quotient topology
on the set of its coadjoint orbits.
The research of M. B. was partially supported by NSF grant DMS-0401164. 相似文献
20.
We propose a notion of algebra of twisted chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess
families of modules depending on infinitely many complex parameters, which we classify in terms of the corresponding algebra
of twisted differential operators. If the underlying manifold is a flag manifold, our construction recovers modules over an
affine Lie algebra parameterized by opers over the Langlands dual Lie algebra. The spaces of global sections of “smallest”
such modules are irreducible
[^(\mathfrakg)]{{\hat{{\mathfrak{g}}}}} -modules, and all irreducible
\mathfrakg{{\mathfrak{g}}} -integrable
[^(\mathfrakg)]{{\hat{{\mathfrak{g}}}}} -modules at the critical level arise in this way. 相似文献