共查询到20条相似文献,搜索用时 31 毫秒
1.
Dan Yasaki 《Selecta Mathematica, New Series》2006,12(3-4):541-564
Let X = Γ \G/ K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has
-rank 1, we construct Γ-equivariant deformation retractions of D = G/K onto a set D0. We prove that D0 is a spine, having dimension equal to the virtual cohomological dimension of Γ. In fact, there is a (k − 1)-parameter family of such deformation retractions, where k is the number of Γ -conjugacy classes of rational parabolic subgroups of G. The construction of the spine also gives a way to construct an exact fundamental domain for Γ. 相似文献
2.
3.
Yasutsugu Fujita 《manuscripta mathematica》2005,118(3):339-360
Let E be an elliptic curve over Q and p a prime number. Denote by Qp,∞ the Zp-extension of Q. In this paper, we show that if p≠3, then where E(Qp,∞)(2) is the 2-primary part of the group E(Qp,∞) of Qp,∞-rational points on E. More precisely, in case p=2, we completely classify E(Q2,∞)(2) in terms of E(Q)(2); in case p≥5 (or in case p=3 and E(Q)(2)≠{O}), we show that E(Qp,∞)(2)=E(Q)(2). 相似文献
4.
Jilali Assim 《manuscripta mathematica》1995,86(1):499-518
In this paper, we give a codescent criterion for the higher tame kernelK
2i
−2/ét
O
E
for a Galoisp-extensionE/F of algebraic number fields (p odd). As an application, we give fori∈ℤ a “going-up” theorem for certain property called (p, i)-regularity, which allows us in particular to construct examples of number fields verifying “twisted” Leopoldt conjectures.
相似文献
5.
Ki-ichiro Hashimoto 《manuscripta mathematica》1999,98(2):165-182
We construct a parametric family {E
(±)(s,t,u)} of minimal Q-curves of degree 5 over the quadratic fields Q
, and the family {C(s,t,u)} of genus two curves over Q covering E
{(+)(s,t,u) whose jacobians are abelian surfaces of GL2-type. We also discuss the modularity for them and the sign change between E
{(+)(s,t,u) and its twist E
(−)(s,t,u), which correspond by modularity to cusp forms of trivial and non-trivial Neben type characters, respectively. We find in
{C(s,t,u)} concrete equations of curves over Q whose jacobians are isogenous over cyclic quartic fields to Shimura's abelian surfaces A
f
attached to cusp forms of
Neben type character of level N= 29, 229, 349, 461, and 509.
Received: 23 September 1997 / Revised version: 26 May 1998 相似文献
6.
A. I. Perov 《Functional Analysis and Its Applications》2010,44(1):69-72
Let M be a complete K-metric space with n-dimensional metric ρ(x, y): M × M → R
n
, where K is the cone of nonnegative vectors in R
n
. A mapping F: M → M is called a Q-contraction if ρ (Fx,Fy) ⩽ Qρ (x,y), where Q: K → K is a semi-additive absolutely stable mapping. A Q-contraction always has a unique fixed point x* in M, and ρ(x*,a) ⩽ (I - Q)-1 ρ(Fa, a) for every point a in M. The point x* can be obtained by the successive approximation method x
k
= Fx
k-1, k = 1, 2,..., starting from an arbitrary point x
0 in M, and the following error estimates hold: ρ (x*, x
k
) ⩽ Q
k
(I - Q)-1ρ(x
1, x
0) ⩽ (I - Q)-1
Q
k
ρ(x
1, x
0), k = 1, 2,.... Generally the mappings (I - Q)-1 and Q
k
do not commute. For n = 1, the result is close to M. A. Krasnosel’skii’s generalized contraction principle. 相似文献
7.
Marco Andreatta Elena Chierici Gianluca Occhetta 《Central European Journal of Mathematics》2004,2(2):272-293
Let X be a Fano variety of dimension n, pseudoindex i
X
and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i
X
−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i
X
≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds
if X has dimension five. 相似文献
8.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1998,89(1):976-987
We solve the problems on the maximum of the conformal radius R(D,1) in the family D(R0) of all simply connected domains D ⊃ ℂ containing the points 0 and 1 and having a fixed value of the conformal radius R(D,0)=R0, and in the family D(R0, ρ) of domains from D(R0) with given hyperbolic distance ρ=ρD(0,1) between 0 and 1. Analogs of the mentioned problems for doubly-connected domains with given conformal module are considered.
Solution of the above problems is based on results of general character in the theory of problems of extremal decomposition
and related module problems. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 93–108. 相似文献
9.
In this paper we show that the Taylor coefficients of a Hecke eigenform at a CM-point, suitably modified, form a sequence
of algebraic numbers that satisfy the Kubota–Leopoldt generalization of the Kummer congruences for primes that split in the
imaginary quadratic field associated with a CM-point. More generally, we show that these numbers are moments of a certain
p-adic measure. In addition, we write down explicitly the “Euler factor” at p in terms of the p th Hecke eigenvalue of the modular form in question and certain data of the CM-point.
P. Guerzhoy is supported by NSF grant DMS-0700933. 相似文献
10.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
11.
We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [Combinatorica, 1995]. For
a graph G, let dim(G) be the smallest d such that G occurs as a (not necessarily induced) subgraph of ℤ∞
d
, the infinite graph with vertex set ℤ
d
and an edge (u, v) whenever ∥u − v∥∞ = 1. The growth rate of G, denoted ρ
G
, is the minimum ρ such that every ball of radius r > 1 in G contains at most r
ρ
vertices. By simple volume arguments, dim(G) = Ω(ρ
G
). Levin conjectured that this lower bound is tight, i.e., that dim(G) = O(ρ
G
) for every graph G.
Previously, it was unknown whether dim(G) could be bounded above by any function of ρ
G
. We show that a weaker form of Levin’s conjecture holds by proving that dim(G) = O(ρ
G
log ρ
G
) for any graph G. We disprove, however, the specific bound of the conjecture and show that our upper bound is tight by exhibiting graphs for
which dim(G) = Ω(ρ
G
log ρ
G
). For several special families of graphs (e.g., planar graphs), we salvage the strong form, showing that dim(G) = O(ρ
G
). Our results extend to a variant of the conjecture for finite-dimensional Euclidean spaces posed by Linial and independently
by Benjamini and Schramm.
Supported by NSF grant CCR-0121555 and by an NSF Graduate Research Fellowship. 相似文献
12.
Masataka Chida 《Archiv der Mathematik》2007,89(3):211-215
For i = 1,
, r, let f
i
be newforms of weight 2k
i
for Γ0(N
i
) with trivial character. We consider the simultaneous non-vanishing problem for the central values of twisted L-functions of f
i
. By using the Shimura correspondence, we give a certain relation between this problem and the kernel fields of 2-adic Galois
representations associated to modular forms.
Received: 28 January 2006 相似文献
13.
Henri Darmon 《Inventiones Mathematicae》1992,110(1):123-146
Summary In [MT1], Mazur and Tate present a refined conjecture of Birch and Swinnerton-Dyer type for a modular elliptic curveE. This conjecture relates congruences for certain integral homology cycles onE(C) (the modular symbols) to the arithmetic ofE overQ. In this paper we formulate an analogous conjecture forE over a suitable imaginary quadratic fieldK, in which the role of the modular symbols is played by Heegner points. A large part of this conjecture can be proved, thanks to the ideas of Kolyvagin on the Euler system of Heegner points. In effect the main result of this paper can be viewed as a generalization of Kolyvagin's result relating the structure of the Selmer group ofE overK to the Heegner points defined in the Mordell-Weil groups ofE over ring class fields ofK. An explicit application of our method to the Galois module structure of Heegner points is given in Sect. 2.2.Oblatum 19-XII-1991, & 25-II-1992 相似文献
14.
Ritabrata Munshi 《Journal of Number Theory》2007,125(1):254-266
A question of Mazur asks whether for any non-constant elliptic fibration {Er}r∈Q, the set {r∈Q:rank(Er(Q))>0}, if infinite, is dense in R (with respect to the Euclidean topology). This has been proved to be true for the family of quadratic twists of a fixed elliptic curve by a quadratic or a cubic polynomial. Here we settle Mazur's question affirmatively for the general quadratic and cubic fibrations. Moreover we show that our method works when Q is replaced by any real number field. 相似文献
15.
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an R-module M, we show that M is Gorenstein injective if and only if Hom
R
(Ȓ,M) belongs to Auslander category B(Ȓ), M is cotorsion and Ext
i
R
(E,M) = 0 for all injective R-modules E and all i > 0.
Received: 24 August 2006 Revised: 30 October 2006 相似文献
16.
Tom Cheatham 《Israel Journal of Mathematics》1979,33(2):172-176
R will denote a commutative integral domain with quotient fieldQ. A torsion-free cover of a moduleM is a torsion-free moduleF and anR-epimorphism σ:F→M such that given any torsion-free moduleG and λ∈Hom
R
(G, M) there exists μ∈Hom
R
(G,F) such that σμ=λ. It is known that ifM is a maximal ideal ofR, R→R/M is a torsion-free cover if and only ifR is a maximal valuation ring. LetE denote the injective hull ofR/M thenR→R/M extends to a homomorphismQ→E. We give necessary and sufficient conditions forQ→E to be a torsion-free cover. 相似文献
17.
18.
W. A. J. Luxemburg 《Israel Journal of Mathematics》1976,25(3-4):189-201
It is shown that the nonarchimedean valuation fieldsρ
R introduced by A. Robinson are not only complete but are also spherically complete. Further-more, it is shown that to every
normed linear space over the reals there exists a nonarchimedean normed linear spaceρ
E overρ
R in the sense of Monna which is spherically complete and extendsE.
Dedicated to the memory of A. Robinson.
Work on this paper was supported in part by NSF Grant MPS 74-17845 相似文献
19.
Benjamin Howard 《Journal of Number Theory》2006,117(2):406-438
Building on ideas of Vatsal [Uniform distribution of Heegner points, Invent. Math. 148(1) (2002) 1-46], Cornut [Mazur's conjecture on higher Heegner points, Invent. Math. 148(3) (2002) 495-523] proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E/Q as one ascends the anticyclotomic Zp-extension of a quadratic imaginary extension K/Q. In the present article, Cornut's result is extended by replacing the elliptic curve E with the Galois cohomology of Deligne's two-dimensional ?-adic representation attached to a modular form of weight 2k>2, and replacing the family of Heegner points with an analogous family of special cohomology classes. 相似文献
20.
Jung Kyu Canci 《Monatshefte für Mathematik》2006,149(4):265-287
Let K be a number field and S a fixed finite set of places of K containing all the archimedean ones. Let R
S
be the ring of S-integers of K. In the present paper we study the cycles in
for rational maps of degree ≥2 with good reduction outside S. We say that two ordered n-tuples (P
0, P
1,… ,P
n−1) and (Q
0, Q
1,… ,Q
n−1) of points of
are equivalent if there exists an automorphism A ∈ PGL2(R
S
) such that P
i
= A(Q
i
) for every index i∈{0,1,… ,n−1}. We prove that if we fix two points
, then the number of inequivalent cycles for rational maps of degree ≥2 with good reduction outside S which admit P
0, P
1 as consecutive points is finite and depends only on S and K. We also prove that this result is in a sense best possible. 相似文献