共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider self-affine tiling substitutions in Euclidean space and the corresponding tiling dynamical systems. It is well
known that in the primitive case, the dynamical system is uniquely ergodic. We investigate invariant measures when the substitution
is not primitive and the tiling dynamical system is non-minimal. We prove that all ergodic invariant probability measures
are supported on minimal components, but there are other natural ergodic invariant measures, which are infinite. Under some
mild assumptions, we completely characterize σ-finite invariant measures which are positive and finite on a cylinder set. A key step is to establish recognizability of
non-periodic tilings in our setting. Examples include the “integer Sierpiński gasket and carpet” tilings. For such tilings,
the only invariant probability measure is supported on trivial periodic tilings, but there is a fully supported σ-finite invariant measure that is locally finite and unique up to scaling. 相似文献
2.
Gebhard Böckle 《manuscripta mathematica》1998,96(2):231-246
We will study the generic fiber over of the universal deformation ring R
Q
, as defined by Mazur, for deformations unramified outside a finite set of primes Q of a given Galois representation , E a number field, k a finite field of characteristic l. The main result will be that, if ˉρ is tame and absolutely irreducible, and if one assumes the Leopoldt conjecture for the
splitting field E
0 of , then defines a smooth l-adic analytic variety, near the trivial lift ρ0 of ˉρ, whose dimension is given by cohomological constraints and as predicted by Mazur. As a corollary it follows that, in
the cases considered here, R
Q
is a quotient of by an ideal I generated by exactly m equations, where and . Under the above assumptions for and ˉρ odd, using ideas of Coleman, Gouvêa and Mazur it should now be possible to show that modular points are Zariski-dense
in the component of , that contains the trivial lift ρ0, provided this lift satisfies the Artin conjecture and E
0 satisfies the Leopoldt conjecture.
Furthermore, in the Borel case, we show that the Krull dimension of R
Q
can exceed any given number, provided Q is chosen appropriately. At the same time, we present some evidence that despite this fact, one might however expect that
the dimension of the generic fiber is given by the same cohomological formula as in the tame case.
Received: 12 December 1997 / Revised version: 5 February 1998 相似文献
3.
Given a projective scheme X over a field k, an automorphism σ: X → X, and a σ-ample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X, L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum
of B, as well as that of other closely related algebras such as skew and skew-Laurent extensions of commutative algebras. Over
an algebraically closed, uncountable field k of characteristic zero, we prove that the primitive ideals of B are characterized by the usual Dixmier-Moeglin conditions whenever dim X ≤ 2. 相似文献
4.
R. Piergallini 《Commentarii Mathematici Helvetici》1992,67(1):287-292
We prove the following theorem: for any closed orientable 3-manifoldM and any homotopy 3-sphere Σ, there exists a simple 3-fold branched coveringp:M→Σ.
We also propose the conjecture that, for any primitive branched coveringp:M→N between orientable 3-manifolds,g(M)≥g(N), whereg denotes the Heegaard genus. By the above mentioned result, the genus 0 case of such conjecture is equivalent to the Poincaré
conjecture. 相似文献
5.
We study the question of which torsion subgroups of commutative algebraic groups over finite fields are contained in modular
difference algebraic groups for some choice of a field automorphism. We show that if G is a simple commutative algebraic group over a finite field of characteristic p, ? is a prime different from p, and for some difference closed field (?, σ) the ?-primary torsion of G(?) is contained in a modular group definable in (?, σ), then it is contained in a group of the form {x∈G(?) :σ(x) =[a](x) } with a∈ℕ\p
ℕ. We show that no such modular group can be found for many G of interest. In the cases that such equations may be found, we recover an effective version of a theorem of Boxall.
Received: 28 May 1998 / Revised version: 20 December 1998 相似文献
6.
OUYANG Yi Department of Mathematical Sciences Tsinghua University Beijing China 《中国科学A辑(英文版)》2005,48(12):1609-1617
We study the Gross conjecture for the cyclotomic function field extension k(∧f)/k where k = Fq(t) is the rational function field and f is a monic polynomial in Fq[t]. We prove the conjecture in the Fermat curve case(i.e., when f = t(t - 1)) by a direct calculation. We also prove the case when f is irreducible, which is analogous to the Weil reciprocity law. In the general case, we manage to show the weak version of the Gross conjecture here. 相似文献
7.
Let A be an Artin group with standard generating set {σ
s
:s∈S}. Tits conjectured that the only relations in A amongst the squares of the generators are consequences of the obvious ones, namely that σ
s
2 and σ
t
2 commute whenever σ
s
and σ
t
commute, for s,t∈S. In this paper we prove Tits’ conjecture for all Artin groups. In fact, given a number m
s
≥2 for each s∈S, we show that the elements {T
s
=σ
s
ms
:s∈S} generate a subgroup that has a finite presentation in which the only defining relations are that T
s
and T
t
commute if σ
s
and σ
t
commute.
Oblatum 21-III-2000 & 1-XII-2000?Published online: 5 March 2001 相似文献
8.
Antonio Kirson 《Annali dell'Universita di Ferrara》2010,56(2):327-333
An automorphism σ of a projective variety X is said to be wild if σ(Y) ≠ Y for every non-empty subvariety
Y \subsetneq X{Y \subsetneq X} . In [1] Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that if X is an irreducible projective variety admitting a wild automorphism then X is an abelian variety, and proved this conjecture for dim(X) ≤ 2. As a step toward answering this conjecture in higher dimensions we prove a structure theorem for projective varieties
of Kodaira dimension 0 admitting wild automorphisms. This essentially reduces the Kodaira dimension 0 case to a study of Calabi-Yau
varieties, which we also investigate. In support of this conjecture, we show that there are no wild automorphisms of certain
Calabi-Yau varieties. 相似文献
9.
LetG be a finite primitive linear group over a fieldK, whereK is a finite field or a number field. We bound the composition length ofG in terms of the dimension of the underlying vector space and of the degree ofK over its prime subfield. As a byproduct, we prove a result of number theory which bounds the number of prime factors (counting
multiplicities) ofq
n−1, whereq, n>1 are integers, improving a result of Turull and Zame [6]. 相似文献
10.
Bin Yong SUN 《数学学报(英文版)》2008,24(2):305-310
The torsion conjecture says: for any abelian variety A defined over a number field k, the order of the torsion subgroup of A(k) is bounded by a constant C(k,d) which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over Q,Г is a torsion subgroup of G(k). Then the order of Г is bounded by a constant C'(k, d) which depends only on k and the dimension d of G. 相似文献
11.
Nikita A. Karpenko 《Transformation Groups》2005,10(2):211-215
We prove Berhuy-Reichstein's conjecture on the
canonical dimension of orthogonal groups showing
that for any integer n ≥ 1, the canonical
dimension of SO2n+1 and of SO2n+2 is equal to n(n + 1)/2. More precisely, for a given
(2n + 1)-dimensional quadratic form φ defined
over an arbitrary field F of characteristic
≠ 2, we establish a certain property of the
correspondences on the orthogonal grassmannian X
of n-dimensional totally isotropic subspaces of
φ, provided that the degree over F of any
finite splitting field of φ is divisible by
2n; this property allows us to prove that the
function field of X has the minimal transcendence
degree among all generic splitting fields of φ. 相似文献
12.
D. Kazhdan 《Israel Journal of Mathematics》1977,28(4):272-286
LetG be a reductive group over a finite fieldk of a characteristicp. Π:G
k → AutU is an irreducible representation ofG in “a general position”. Springer formulated a conjecture about values of the character of Π on unipotent elements. This
conjecture is proved in the article. 相似文献
13.
Olivier Brunat 《Mathematische Zeitschrift》2009,263(2):411-424
This note is concerned with the McKay conjecture in the representation theory of finite groups. Recently, Isaacs–Malle–Navarro
have shown that, in order to prove this conjecture in general, it is sufficient to establish certain properties of all finite
simple groups. In this note, we develop some new methods for dealing with these properties for finite simple groups of Lie
type in the defining characteristic case. We apply these methods to show that the Suzuki and Ree groups, G
2(q), F
4(q) and E
8(q) have the required properties. 相似文献
14.
For an odd prime p we construct an infinite class of non-isomorphic Hopf algebras of dimension p
4 over an infinite field containing primitive p-th roots of unity, answering in the negative a long standing conjecture of Kaplansky.
Oblatum 6-XI-1997 / Published online: 12 November 1998 相似文献
15.
H. A. Jung 《Combinatorica》1981,1(3):285-288
Results involving automorphisms and fragments of infinite graphs are proved. In particular for a given fragmentC and a vertex-transitive subgroupG of the automorphism group of a connected graph there exists σ≠G such that σ[C] ⊂C. This proves the countable case of a conjecture of L. Babai and M. E. Watkins concerning graphs allowing a vertex-transitive
torsion group action.
Dedicated to Prof. K. Wagner on his 70th birthday 相似文献
16.
We introduce μ-convexity, a new kind of game convexity defined on a σ-algebra of a nonatomic finite measure space. We show that μ-convex games are μ-average monotone. Moreover, we show that μ-average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results
to the problem of partitioning a measurable space among a finite number of individuals. For this problem, we extend some results
known for the case of individuals’ preferences that are representable by nonatomic probability measures to the more general
case of nonadditive representations. 相似文献
17.
Eli Aljadeff 《Israel Journal of Mathematics》2012,189(1):189-205
Let W be an associative PI — algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W e ) denote the codimension growth of W and of the identity component W e , respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ |G|2 exp(W e ). The inequality is known in case the algebra W is affine (i.e., finitely generated). Here we prove the conjecture in general. 相似文献
18.
Burkhard Külshammer 《Israel Journal of Mathematics》1995,92(1-3):295-306
Donovan’s conjecture, on blocks of finite group algebras over an algebraically closed field of prime characteristicp, asserts that for any finitep-groupD, there are only finitely many Morita equivalence classes of blocks with defect groupD. The main result of this paper is a reduction theorem: It suffices to prove the conjecture for groups generated by conjugates
ofD. A number of other finiteness results are proved along the way. The main tool is a result on actions of algebraic groups. 相似文献
19.
Let f be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map σ f of a finite-dimensional Teichmüller space. We prove that this map extends continuously to the augmented Teichmüller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston’s pullback map near invariant strata of the boundary of the augmented Teichmüller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston’s pullback map. Our approach also yields new proofs of Thurston’s theorem and Pilgrim’s Canonical Obstruction theorem. 相似文献
20.
Walter Gubler 《Inventiones Mathematicae》2007,169(2):377-400
We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang’s proof of the number field case replacing the complex analytic tools by tropical analytic
geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place v. As a corollary, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over
v. 相似文献