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1.
Jack Sonn 《Israel Journal of Mathematics》2000,119(1):1-8
Letp be a prime and let ℚ(p) denote the maximalp-extension of ℚ. We prove that for every primep, the free pro-p group on countably many generators is realizable as a regular extension of ℚ(p)(t). As a consequence, if ℚ
nil
denotes the maximal nilpotent extension of ℚ, then every finite nilpotent group is realizable as a regular extension of ℚ
nil
(t). 相似文献
2.
Let Γ
g, n
be the mapping class group of a compact Riemann surface of genusg withn points preserved (2−2g−n<0,g≥1,n≥0). The Torelli subgroup of Γ
g, n
has a natural weight filtration {Γg, n(m)}
m≥1. Each graded quotient gr
m
Γ
g, n
⊗ ℚ (m≥1) is a finite dimensional vector space over ℚ on which the group Sp(2g, ℚ)×S
n
naturally acts.
In this paper, we have determined the Sp(2g, ℚ)×S
n
module structure of gr
m
Γ
g, n
⊗ ℚ for 1≤m≤3. This includes a verification of an expectation by S. Morita. Also, for generalm, we have identified a certain Sp(2g, ℚ)-irreducible component of gr
m
Γ
g, n
⊗ ℚ by constructing explicitly elements in these modules. 相似文献
3.
We study the classification of elliptic curves E over the rationals ℚ according to the torsion sugroups E
tors(ℚ). More precisely, we classify those elliptic curves with E
tors(ℚ) being cyclic with even orders. We also give explicit formulas for generators of E
tors(ℚ). These results, together with the recent results of K. Ono for the non-cyclic E
tors(ℚ), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.
Received July 29, 1999, Revised March 9, 2001, Accepted July 20, 2001 相似文献
4.
Xiao Yun CHENG Jian Guo XIA Hou Rong QIN 《数学学报(英文版)》2007,23(5):819-826
Let K2 be the Milnor functor and let Фn (x)∈ Q[X] be the n-th cyclotomic polynomial. Let Gn(Q) denote a subset consisting of elements of the form {a, Фn(a)}, where a ∈ Q^* and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn(Q) is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn(Q) is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h(Q(ζp)) is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105. 相似文献
5.
Jack Sonn 《Israel Journal of Mathematics》1994,85(1-3):391-405
Let ℚ
ab
denote the maximal abelian extension of the rationals ℚ, and let ℚabnil denote the maximal nilpotent extension of ℚ
ab
. We prove that for every primep, the free pro-p group on countably many generators is realizable as the Galois group of a regular extension of ℚabnil(t). We also prove that ℚabnil is not PAC (pseudo-algebraically closed).
This paper was inspired by the author's participation in a special year on the arithmetic of fields at the Institute for Advanced
Studies at the Hebrew University of Jerusalem. I would like to express my appreciation to the Institute for its hospitality,
and to the organizers, especially Moshe Jarden.
Partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund-Japan Technion
Society Research Fund. 相似文献
6.
Fumihito Oda 《Algebras and Representation Theory》2010,13(2):231-242
Let p be a prime number. This paper solves the question of the difference between the rank of the crossed Burnside ring B
c
(P) of a finite p-group P and of the rational representation ring
R\mathbbQ (D(P))R_{{\mathbb{Q}}} (\mathcal{D}(P)) of the Drinfel’d double D(P)\mathcal{D}(P) of the group algebra ℚ P. The difference is represented by using the Dade groups of certain subgroups of P. 相似文献
7.
Xian Zu Lin 《数学学报(英文版)》2011,27(5):863-870
Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l
k
: H*(G/P, ℚ) → H*(G/P, ℚ), l
k
(u) = k
i
u, u ∈ H
2i
(G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l
k
can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary. 相似文献
8.
Benjamin Schraen 《Israel Journal of Mathematics》2010,176(1):307-361
We construct some locally ℚ
p
-analytic representations of GL2(L), L a finite extension of ℚ
p
, associated to some p-adic representations of the absolute Galois group of L. We prove that the space of morphisms from these representations to the de Rham complex of Drinfel’d’s upper half space has
a structure of rank 2 admissible filtered (φ, N)-module. Finally, we prove that this filtered module is associated, via Fontaine’s theory, to the initial Galois representation. 相似文献
9.
Hans-Joachim Baues 《Inventiones Mathematicae》1998,132(3):467-489
10.
Christophe Breuil 《Israel Journal of Mathematics》2011,182(1):349-382
Let ρ be a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/ℚ
p
) over ̅F
p
. The modulo p Langlands correspondence for GL2(ℚ
p
) defined in [5], as realized in [9], can be reformulated as a quite simple recipee giving back the (φ, Γ)-module of the dual of ρ starting from the “Diamond diagram” associated to ρ. Let F be a finite unramified extension of ℚ
p
and ρ a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/F) over ̅F
p
. When one formally extends this recipee to the Diamond diagrams associated to ρ in [6], we show that one essentially finds the (φ, Γ)-module of the tensor induction from F to ℚ
p
of the dual of ρ. 相似文献
11.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
12.
Heiko Knospe 《manuscripta mathematica》1995,87(1):225-258
We explain how to associate to an abelian variety over ℚ with good and non-ordinary reduction atp a submodule of some power of a ring of analytic functions over the Iwasawa-algebra. From this construction formulas about
the size of the Selmer groups over the the cyclotomic ℤ
p
of ℚ are deduced. 相似文献
13.
I. Yu. Sukharev 《Moscow University Mathematics Bulletin》2011,66(3):123-124
The well-known Oppenheim expansion algorithm in the field ℚ
p
is generalized to the ring ℚ
g
, where g = p
1 · ... · p
N
. The metric properties of the digits of this expansion and also the metric properties of the coefficients of some expansions
of polyadic numbers are studied. 相似文献
14.
We fix a prime p and let f(X) vary over all monic integer polynomials of fixed degree n. Given any possible shape of a tamely ramified splitting of p in an extension of degree n, we prove that there exists a rational function φ(X)∈ℚ(X) such that the density of the monic integer polynomials f(X) for which the splitting of p has the given shape in ℚ[X]/f(X) is φ(p) (here reducible polynomials can be neglected). As a corollary, we prove that, for p≥n, the density of irreducible monic polynomials of degree n in ℤ
p
[X] is the value at p of a rational function φ
n
(X)∈ℚ(X). All rational functions involved are effectively computable.
Received: 15 September 1998 / Revised version: 21 October 1999 相似文献
15.
The group Aff(ℚ) of affine transformations with rational coefficients acts naturally not only on the real line ℝ, but also
on the p-adic fields ℚp. The aim of this note is to show that all these actions are necessary and sufficient to represent bounded μ-harmonic functions for a probability measure μ on Aff(ℚ) that is supported by a finitely generated subgroup, that is, to describe the Poisson boundary.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional
Analysis, 2007. 相似文献
16.
We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗π
Y, their injective tensor product X ⊗ɛ
Y, or the dual (X ⊗π
Y)* contain complemented copies of ℓp. 相似文献
17.
Sérgio Mota Alves 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):109-124
The verbally prime algebras are well understood in characteristic 0 while over a field of positive characteristic p > 2 little is known about them. In previous papers we discussed some sharp differences between these two cases for the characteristic;
we showed that the so-called Tensor Product Theorem cannot be extended for infinite fields of positive characteristic p > 2. Furthermore we studied the Gelfand-Kirillov dimension of the relatively free algebras of verbally prime and related
algebras. In this paper we compute the GK dimensions of several algebras and thus obtain a new proof of the fact that the
algebras M
a,a
(E) ⊗ E and M
2a
(E) are not PI equivalent in characteristic p > 2. Furthermore we show that the following algebras are not PI equivalent in positive characteristic: M
a,b
(E) ⊗ M
c,d
(E) and M
ac+bd,ad+cb
(E); and M
a,b
(E) ⊗ M
c,d
(E) and M
e, f
(E) ⊗ M
g,h
(E) when a ≥ b, c ≥ d, e ≥ f, g ≥ h, ac + bd = eg+ f h, ad +bc = eh + fg and ac ≠ eg. Here E stands for the infinite dimensional Grassmann algebra with 1, and M
a,b
(E) is the subalgebra of M
a+b
(E) of the block matrices with blocks a × a and b × b on the main diagonal with entries from E
0, and off-diagonal entries from E
1; E = E
0 ⊗ E
1 is the natural grading on E.
Partially supported by CNPq 620025/2006-9. This paper was written during the author’s PhD study at the UNICAMP, under the
supervision of P.Koshlukov, to whom he expresses his sincere thanks. 相似文献
18.
Frank Gerth III 《manuscripta mathematica》1991,70(1):39-50
Letp be an odd prime number, and letK be a cyclic extension of ℚ(ζ) of degreep, where ζ is a primitivep-th root of unity. LetC
K
be thep-class group ofK, and letr
K
be the minimal number of generators ofC
K
1−σ
as a module over Gal(K/ℚ(ζ)), were σ is a generator of Gal(K/ℚ(ζ)). This paper shows how likely it is forr
K
= 0, 1, 2, … whenp=3, 5, or 7, and describes the obstacle to generalizing these results to regular primesp>7. 相似文献
19.
François Ledrappier Mark Pollicott 《Bulletin of the Brazilian Mathematical Society》2005,36(2):143-176
In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚp) on ℚp × ℚp and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually
associated to GL(2,ℚp)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension
of the geodesic flow. 相似文献
20.
The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p
∞-Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/ℚ is semistable at 2 and 3, K/ℚ is abelian and K
∞ is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of
. We also give analogous results when K/ℚ is non-abelian, the base field is not ℚ and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of
finite groups, their “regulator constants”, and compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.
T. Dokchitser is supported by a Royal Society University Research Fellowship. 相似文献