共查询到20条相似文献,搜索用时 15 毫秒
1.
Jayanta Manoharmayum 《Journal of Number Theory》2009,129(5):1178-1190
Let F be a number field. Given a continuous representation with insoluble image we show, under moderate assumptions at primes dividing ?∞, that for some continuous representation which is unramified outside finitely many primes. We also establish level lowering when F is totally real, is the reduction of a nearly ordinary Hilbert modular form and is distinguished at ?. 相似文献
2.
Georgios Pappas 《Mathematische Annalen》2008,341(1):71-97
We use the theory of n-cubic structures to study the Galois module structure of the coherent cohomology groups of unramified Galois covers of varieties
over the integers. Assuming that all the Sylow subgroups of the covering group are abelian, we show that the invariant that
measures the obstruction to the existence of a “virtual normal integral basis” is annihilated by a product of certain Bernoulli
numbers with orders of even K-groups of Z. We also show that the existence of such a basis is closely connected to the truth of the Kummer-Vandiver conjecture for
the prime divisors of the degree of the cover.
Partially supported by NSF grants # DMS05-01049 and # DMS01-11298 (via the Institute for Advanced Study). 相似文献
3.
Chandrashekhar Khare 《manuscripta mathematica》1998,95(1):181-188
We study the multiplicity with which 2-dimensional modp Galois representations occur in Jacobians of modular curves. 相似文献
4.
5.
Hiroyuki Hasebe 《manuscripta mathematica》2002,109(2):151-158
For a field k, We denote the maximal abelian extension of k by k
ab
and (K
ab
r−1
ab
by k
ab
r
. In this paper, unramified Galois extensions over k
ab
r
are constructed using Galois representations of arbitrary dimension with larger coefficient rings.
Received: 31 August 2001 / Revised version: 22 March 2002
Mathematics Subject Classification (2000): 11R21 相似文献
6.
Let k be a number field with ring of integers Ok, and let Γ be the dihedral group of order 8. For each tame Galois extension N/k with group isomorphic to Γ, the ring of integers ON of N determines a class in the locally free class group Cl(Ok[Γ]). We show that the set of classes in Cl(Ok[Γ]) realized in this way is the kernel of the augmentation homomorphism from Cl(Ok[Γ]) to the ideal class group Cl(Ok), provided that the ray class group of Ok for the modulus 4Ok has odd order. This refines a result of the second-named author (J. Algebra 223 (2000) 367-378) on Galois module structure over a maximal order in k[Γ]. 相似文献
7.
In this paper, we study the image of l-adic representations coming from Tate module of an abelian variety defined over a number field. We treat abelian varieties with complex and real multiplications. We verify the Mumford-Tate conjecture for a new class of abelian varieties with real multiplication. 相似文献
8.
9.
Let p be a prime number and K a number field containing a primitive p-th root of unity. It is known that an unramified cyclic extension L/K of degree p has a power integral basis if it has a normal integral basis. We show that for all p, the converse is not true in general. Received: 18 July 2000 / Revised version: 18 October 2000 相似文献
10.
Chandrashekhar Khare 《manuscripta mathematica》1998,95(2):181-188
We study the multiplicity with which 2-dimensional mod p Galois representations occur in Jacobians of modular curves.
Received: 26 February 1997 / Revised version: 2 July 1997 相似文献
11.
Álvaro Lozano-Robledo 《Journal of Number Theory》2010,130(3):539-558
Let K be a quadratic imaginary number field with discriminant DK≠−3,−4 and class number one. Fix a prime p?7 which is unramified in K. Given an elliptic curve A/Q with complex multiplication by K, let be the representation which arises from the action of Galois on the Tate module. Herein it is shown that, for all but finitely many inert primes p, the image of a certain deformation of is “as large as possible”, that is, it is the full inverse image of a Cartan subgroup of SL(2,Zp). If p splits in K, then the same result holds as long as a certain Bernoulli-Hurwitz number is a p-adic unit which, in turn, is equivalent to a prime ideal not being a Wieferich place. The proof rests on the theory of elliptic units of Robert and Kubert-Lang, and on the two-variable main conjecture of Iwasawa theory for quadratic imaginary fields. 相似文献
12.
Cristian Virdol 《Journal of Number Theory》2011,131(4):681-684
In this paper we prove that if the Birch and Swinnerton-Dyer conjecture holds for abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character, then the Birch and Swinnerton-Dyer conjecture holds for abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character regarded over arbitrary totally real number fields. 相似文献
13.
M. Godin 《Journal of Number Theory》2003,98(2):320-328
Let k be a number field and Ok its ring of integers. Let Γ be the alternating group A4. Let be a maximal Ok-order in k[Γ] containing Ok[Γ] and its class group. We denote by the set of realizable classes, that is the set of classes such that there exists a Galois extension N/k at most tamely ramified, with Galois group isomorphic to Γ, for which the class of is equal to c, where ON is the ring of integers of N. In this article we determine and we prove that it is a subgroup of provided that k and the 3rd cyclotomic field of are linearly disjoint, and the class number of k is odd. 相似文献
14.
15.
16.
Álvaro Lozano-Robledo 《Journal of Number Theory》2006,117(2):439-470
Let K be a quadratic imaginary number field with discriminant DK≠-3,-4 and class number one. Fix a prime p?7 which is not ramified in K and write hp for the class number of the ray class field of K of conductor p. Given an elliptic curve A/K with complex multiplication by K, let be the representation which arises from the action of Galois on the Tate module. Herein it is shown that if then the image of a certain deformation of is “as big as possible”, that is, it is the full inverse image of a Cartan subgroup of SL(2,Zp). The proof rests on the theory of Siegel functions and elliptic units as developed by Kubert, Lang and Robert. 相似文献
17.
Let K/F be a Kummer cyclic extension of number fields. In the case when the degree is a prime number, Gómez Ayala gave an explicit criterion for the existence of a normal integral basis. More recently Ichimura proposed a generalization of that result for cyclic extensions of arbitrary degree, but we have found that Ichimura’s result is incorrect. In this paper we present a counter-example to Ichimura’s result as well as the correct generalization of Gómez Ayala’s result. 相似文献
18.
J. E. Carter 《Archiv der Mathematik》2003,81(3):266-271
Let K be a number field and let G be a finite abelian group. We call
K a Hilbert-Speiser field of type G if, and only if, every tamely
ramified normal extension L/K with Galois group isomorphic to G has
a normal integral basis. Now let C2 and C3 denote the cyclic
groups of order 2 and 3, respectively. Firstly, we show that among all
imaginary quadratic fields, there are exactly three Hilbert-Speiser
fields of type $C_{2}: \mathbb{Q}(\sqrt {m})$, where $m \in \{-1, -3, -7\}$.
Secondly, we give some necessary and sufficient conditions for a real
quadratic field $K = \mathbb{Q}(\sqrt {m})$ to be a Hilbert-Speiser field of
type C2. These conditions are in terms of the congruence class of m
modulo 4 or 8, the fundamental unit of K, and the class number of K.
Finally, we show that among all quadratic number fields, there are
exactly eight Hilbert-Speiser fields of type $C_{3}: \mathbb{Q}(\sqrt {m})$,
where $m \in \{-11,-3, -2, 2, 5, 17, 41, 89\}$.Received: 2 April 2002 相似文献
19.
Ludwig Gauckler 《Archiv der Mathematik》2008,90(2):136-139
Let p be a rational prime and let a be an integer which is divisible by p exactly to the first power. Then the Galois group of the Eisenstein polynomial f = X
p
+ aX + a is known to be either the full symmetric group S
p
or the affine group A(1, p), and it is conjectured that always G = S
p
. In this note we settle this conjecture for p = 5 and, answering a question by J.-P. Serre, we show that this does not carry over when replacing the integer a by some rational number with 5-adic valuation equal to 1.
Received: 6 June 2007 相似文献
20.
Romyar T. Sharifi 《Mathematische Annalen》2008,342(2):297-308
Let p be an odd prime satisfying Vandiver’s conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z
p
-extensions of Q(μ
p
) and the Galois group of the maximal unramified pro-p extension of Q
. We give a lower bound for the height of the annihilator of X as an Iwasawa module. Under some mild assumptions on Bernoulli numbers, we provide a necessary and sufficient condition for
to be abelian. The bound and the condition in the two results are given in terms of special values of a cup product pairing
on cyclotomic p-units. We obtain in particular that, for p < 1,000, Greenberg’s conjecture that X is pseudo-null holds and is in fact abelian. 相似文献