共查询到20条相似文献,搜索用时 15 毫秒
1.
Michael Larsen 《Journal of Number Theory》2003,101(2):398-403
Let A be an abelian variety over a number field K. If P and Q are K-rational points of A such that the order of the reduction of Q divides the order of the ) reduction of P for almost all prime ideals , then there exists a K-endomorphism φ of A and a positive integer k such that φ(P)=kQ. 相似文献
2.
Following the approach in the archimedean case, we introduce the notion
of admissible metrics for line bundles on curves and abelian varieties
over non-archimedean local fields. Several properties of admissible
metrics are considered and we show that this approach yields the same
notion of admissible metrics over curves as doing harmonic analysis on
the reduction graph of the curve.
Received: 9 September 2002 相似文献
3.
Sachiko Ohtani 《Journal of Number Theory》2006,120(2):272-286
We study the deformation theory of Galois representations whose restriction to every decomposition subgroup is abelian. As an application, we construct unramified non-solvable extensions over the field obtained by adjoining all p-power roots of unity to the field of rational numbers. 相似文献
4.
Takao Yamazaki 《Journal of Number Theory》2003,99(2):298-306
5.
6.
We consider the support problem of Erdös in the context of l-adic representations of the absolute Galois group of a number field. Main applications of the results of the paper concern Galois cohomology of the Tate module of abelian varieties with real and complex multiplications, the algebraic K-theory groups of number fields and the integral homology of the general linear group of rings of integers. We answer the question of Corrales-Rodrigáñez and Schoof concerning the support problem for higher dimensional abelian varieties. 相似文献
7.
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
8.
We introduce and study a new way to categorize supersingular abelian varieties defined over a finite field by classifying them as fully maximal, mixed or fully minimal. The type of A depends on the normalized Weil numbers of A and its twists. We analyze these types for supersingular abelian varieties and curves under conditions on the automorphism group. In particular, we present a complete analysis of these properties for supersingular elliptic curves and supersingular abelian surfaces in arbitrary characteristic, and for a one-dimensional family of supersingular curves of genus 3 in characteristic 2. 相似文献
9.
Marc-Hubert Nicole 《Journal of Number Theory》2008,128(11):2874-2889
Let p be an unramified prime in a totally real field L such that h+(L)=1. Our main result shows that Hilbert modular newforms of parallel weight two for Γ0(p) can be constructed naturally, via classical theta series, from modules of isogenies of superspecial abelian varieties with real multiplication on a Hilbert moduli space. This may be viewed as a geometric reinterpretation of the Eichler Basis Problem for Hilbert modular forms. 相似文献
10.
Let L be a totally real field of strict class number one and let OL be its ring of integers. Let p be a rational prime which is unramified in L. We consider the distance between two superspecial abelian varieties with real multiplication in characteristic p, where by “distance” we mean the minimal degree of an OL-isogeny. We give upper and lower bounds on the distance between superspecial abelian varieties with real multiplication by L in characteristic p in terms of p and the degree and discriminant of L. 相似文献
11.
12.
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
13.
J. Huisman 《manuscripta mathematica》1994,85(1):165-175
Supported by the Netherlands Organisation for Scientific Research (NWO) 相似文献
14.
Richard Pink 《Journal of Number Theory》2006,116(2):348-372
Let φ be a Drinfeld A-module in special characteristic p0 over a finitely generated field K. For any finite set P of primes p≠p0 of A let ΓP denote the image of Gal(Ksep/K) in its representation on the product of the p-adic Tate modules of φ for all p∈P. We determine ΓP up to commensurability. 相似文献
15.
Richard Pink 《Journal of Number Theory》2006,116(2):324-347
Let ? be a Drinfeld A-module of rank r over a finitely generated field K. Assume that ? has special characteristic p0 and consider any prime p≠p0 of A. If EndKsep(?)=A, we prove that the image of Gal(Ksep/K) in its representation on the p-adic Tate module of ? is Zariski dense in GLr. 相似文献
16.
Alexis Michel 《Mathematische Zeitschrift》1999,230(3):451-470
Let E be an elliptic curve with complex multiplication over the ring of integers of an imaginary quadratic field K. Denote by p an odd prime that splits into in and by the unique -extension of K totally ramified above . It is well-known that the Selmer group attached to any finite extension of is analogous to the minus part of the p-class group of divisors of the cyclotomic - extensions of CM number fields. One of the most striking examples of this analogy is the existence of a translation formula à la Kida for the codimension of the Selmer group at the top of the tower. In this article we carry on the analogy with the presentations
of results similar to those proven by Gold and Madan in the cyclotomic case (see [8]), which were the continuation of Kida's
work. More precisely, we describe the -structure of the Selmer group when G is a cyclic group of order p or . In addition, we study the modular representation of G on the subgroup of points of order p of the Selmer group, when G is cyclic of order .
Received December 3, 1997 相似文献
17.
Nguyêñ Quôć Thǎńg 《Mathematische Zeitschrift》2008,259(2):457-467
We treat a case that was omitted from consideration in our article [2] in Math Zeit, 2007. 相似文献
18.
Louboutin Stéphane 《manuscripta mathematica》1996,91(1):343-352
Lately, I. Miyada proved that there are only finitely many imaginary abelian number fields with Galois groups of exponents
≤2 with one class in each genus. He also proved that under the assumption of the Riemann hypothesis there are exactly 301
such number fields. Here, we prove the following finiteness theorem: there are only finitely many imaginary abelian number
fields with one class in each genus. We note that our proof would make it possible to find an explict upper bound on the discriminants
of these number fields which are neither quadratic nor biquadratic bicyclic. However, we do not go into any explicit determination. 相似文献
19.
Takashi Kawamura 《Commentarii Mathematici Helvetici》2003,78(3):486-493
Mod l Galois representations of
1- and 2-dimensional abelian varieties with trivial endomorphism ring are
surjective for sufficiently large prime l
as Serre proved. But he did not give an effective lower bound of
l
0 such that
they are surjective for l >
l
0.
We supply an effective evaluation of
l
0 by an
elementary proof of the surjectivity. The proof
uses the Masser-Wüstholz theorem and Kleidman and Liebecks
classification of the maximal subgroups of
GL
2
F
l
)
and GSp
4
(F
l
). 相似文献
20.
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