共查询到20条相似文献,搜索用时 0 毫秒
1.
Ribet [Ri] has generalized the conjecture of Shimura–Taniyama–Weil to abelian varieties defined over Q,giving rise to the study of abelian varieties of GL2-type. In this context, all curves over Q of genus one have Jacobian variety of GL2-type. Our aim in this paper is to begin with the analysis of which curves of genus 2 have Jacobian variety of GL2-type. To this end, we restrict our attention to curves with rational Rosenhain model and non-abelian automorphism group,
and use the embedding of this group into the endomorphism algebra of its Jacobian variety to determine if it is of GL2-type.
Received: 31 March 1998 / Revised version: 29 June 1998 相似文献
2.
3.
Pavlos Tzermias 《manuscripta mathematica》1998,97(4):483-488
We determine all algebraic points of degree at most five over Q on the Fermat curve of degree seven.
Received: 26 February 1998 / Revised version: 1 June 1998 相似文献
4.
We discuss a technique for trying to find all rational points on curves of the form Y
2=f
3
X
6+f
2
X
4+f
1
X
2+f
0, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or
1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this
case, we shall derive an associated family of elliptic curves, defined over a number field ℚα. If each of these elliptic
curves has rank less than the degree of ℚα :
ℚ, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over ℚα) on the elliptic curves, for which x∈ℚ. This in turn allows us to find all ℚ-rational points on the original genus 2 curve. We apply this to give a solution to
a problem of Diophantus (where the sextic in X is irreducible over ℚ), which simplifies the recent solution of Wetherell. We also present two examples where the sextic
in X is reducible over ℚ.
Received: 27 November 1998 / Revised version: 4 June 1999 相似文献
5.
6.
Mohamed Saïdi 《Mathematische Annalen》1998,312(4):625-639
7.
8.
F. J. Cirre 《manuscripta mathematica》2000,101(4):495-512
For each integer g≥ 3 we give the complete list of groups acting as full automorphism groups of real algebraic curves of genus $g$ which are
double covers of the real projective plane. Explicit polynomial equations of such curves and the formulae of their automorphisms
are also given.
Received: 29 April 1999 / Revised version: 26 November 1999 相似文献
9.
Daniel Allcock 《Mathematische Annalen》2000,317(3):483-488
10.
Richard Pink 《manuscripta mathematica》2000,102(1):1-24
Let X be an irreducible smooth projective curve over an algebraically closed field of characteristic p>0. Let ? be either a finite field of characteristic p or a local field of residue characteristic p. Let F be a constructible étale sheaf of $\BF$-vector spaces on X. Suppose that there exists a finite Galois covering π:Y→X such that the generic monodromy of π*
F is pro-p and Y is ordinary. Under these assumptions we derive an explicit formula for the Euler–Poincaré characteristic χ(X,F) in terms of easy local and global numerical invariants, much like the formula of Grothendieck–Ogg–Shafarevich in the case
of different characteristic. Although the ordinariness assumption imposes severe restrictions on the local ramification of
the covering π, it is satisfied in interesting cases such as Drinfeld
modular curves.
Received: 7 December 1999 / Revised version: 28 January 2000 相似文献
11.
12.
Riccardo Salvati Manni 《manuscripta mathematica》2000,101(2):267-269
In this paper we prove the existence of cusp forms relative to the full modular group whose genus is equal to the weight.
These cusp forms are linear combination of theta series.
Received: 26 July 1999 / Revised version: 16 September 1999 相似文献
13.
Ravi Vakil 《manuscripta mathematica》2000,102(1):53-84
In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps,
and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count
irreducible curves on Hirzebruch surfaces in a fixed divisor class and of fixed geometric genus, (ii) we compute the higher-genus
Gromov–Witten invariants of (or equivalently, counting curves of any genus and divisor class on) del Pezzo surfaces of degree
at least 3. In the case of the cubic surface in (ii), we first use a result of Graber to enumeratively interpret higher-genus
Gromov–Witten invariants of certain K-nef surfaces, and then apply this to a degeneration of a cubic surface.
Received: 30 June 1999 / Revised version: 1 January 2000 相似文献
14.
15.
Kentaro Yoshitomi 《manuscripta mathematica》1998,96(1):37-66
The canonical height on an abelian variety is useful and important for the study of the Mordell-Weil group. But it is difficult
to calculate the canonical height in general. We give an effective method to calculate the canonical height on a Jacobian
surface. As an application, we verify the Birch-Swinnerton-Dyer conjecture for the Jacobian surface of a twisted modular curve.
Received: 15 July 1996 / Revised version: 19 January 1997 相似文献
16.
In this paper we analyze the integral of the star-product of (n+1) Green currents associated to (n+1) global sections of an ample line bundle equipped with a translation invariant metric over an n-dimensional, polarized abelian variety. The integral is shown to equal the logarithm of the Petersson norm of a certain Siegel
modular form, which is explicitly described in terms of the given data. This result can be interpreted as evaluating an archimedian
height on a family of polarized abelian varieties. The key ingredient to the proof of the main formula is a dd
c
-variational formula for the integral under consideration. In the case of dimensions n=1,2,3 explicit examples in terms of classical Riemann theta functions are given.
Received: 13 February 1998 相似文献
17.
Tyler J. Jarvis 《Mathematische Zeitschrift》2000,235(1):123-149
This article provides two different, but closely related, moduli problems, which in characteristic zero provide a type of
compactification of the universal Picard over the moduli of stable curves. Although neither is of finite type, both are limits
of a sequence of stacks, each of which is a separated algebraic stack of finite type. We discuss relations to previous compactifications
and partial compactifications, give a number of examples related to this compactification, and work out the structure of its
fibres over certain fixed curves. Some applications are also discussed.
Received January 5, 1998; in final form April 1, 1999 / Published online July 3, 2000 相似文献
18.
We study the slopes of Frobenius on the rigid cohomology and the rigid cohomology with compact support of an algebraic variety over a perfect field of positive characteristic. We then prove that any unipotent overconvergent F-isocrystal on a smooth variety has a slope filtration whose graded parts are pure. Received: 23 December 1998 / Revised version: 5 July 1999 相似文献
19.
Fabien Trihan 《manuscripta mathematica》1998,96(4):397-419
The purpose of this article is to give a cohomological formula for the unit-root part of the L-function associated to a Barsotti-Tate group G on a scheme S over a field of characteristic p when G extends to some compactification of S. This is an analogue of a part of a conjecture of Katz according to wich the L-function of an F-crystal should be expressed in terms of the p-adic etale sheaf corresponding to the unit-root part of the crystal. In order to carry out this project, we use the technics
of [E-LS II] wich require in our case an extension of the Dieudonné crystalline theory ([B-B-M]) to “crystal of level mG” in the sense of Berthelot. We show that the unit-root L-function of the Dieudonné crystal associated to G can be expressed in terms of the syntomic cohomology of the Ext group of G by the constant sheaf.
Received: 24 March 1997 / Revised version: 6 January 1998 相似文献
20.
Let be a prime. We show that the space of weight one Eisenstein series defines an embedding into ${mathbb P}^{(p-3)/2}X_1(p)$ for the congruence group that is scheme-theoretically cut out by explicit quadratic equations. Received: 8 November 2000 / Published online: 17 August 2001 相似文献