共查询到20条相似文献,搜索用时 15 毫秒
1.
Jakob Stix 《Journal of Pure and Applied Algebra》2011,215(6):1371-1397
We introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension and establish Grothendieck’s section conjecture for an open subset of the Reichardt-Lind curve. 相似文献
2.
Kentaro Mitsui 《Journal of Pure and Applied Algebra》2019,223(2):553-570
We study the Frobenius base change of a torsor under a smooth algebraic group over a field of positive characteristic by relating it to the pushforward of the torsor under the Frobenius homomorphism. As an application, we determine the change of the multiplicity of a closed fiber of an elliptic surface by purely inseparable base changes with respect to the base curve in the case where the generic fiber is supersingular. 相似文献
3.
Let C be an irreducible plane curve. A point P in the projective plane is said to be Galois with respect to C if the function field extension induced by the projection from P is Galois. We denote by δ′(C) the number of Galois points contained in P2?C. In this article we will present two results with respect to determination of δ′(C) in characteristic two. First we determine δ′(C) for smooth plane curves of degree a power of two. In particular, we give a new characterization of the Klein quartic in terms of δ′(C). Second we determine δ′(C) for a generalization of the Klein quartic, which is related to an example of Artin–Schreier curves whose automorphism group exceeds the Hurwitz bound. This curve has many Galois points. 相似文献
4.
Filip Najman 《Journal of Number Theory》2010,130(9):1964-1968
Text
In a previous paper Najman (in press) [9], the author examined the possible torsions of an elliptic curve over the quadratic fields Q(i) and . Although all the possible torsions were found if the elliptic curve has rational coefficients, we were unable to eliminate some possibilities for the torsion if the elliptic curve has coefficients that are not rational. In this note, by finding all the points of two hyperelliptic curves over Q(i) and , we solve this problem completely and thus obtain a classification of all possible torsions of elliptic curves over Q(i) and .Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=VPhCkJTGB_o. 相似文献5.
6.
R. Clement Fernández 《Journal of Pure and Applied Algebra》2009,213(7):1489-1500
Let p≥5 be a prime, ζ a primitive pth root of unity and λ=1−ζ. For 1≤s≤p−2, the smooth projective model Cp,s of the affine curve vp=us(1−u) is a curve of genus (p−1)/2 whose jacobian Jp,s has complex multiplication by the ring of integers of the cyclotomic field Q(ζ). In 1981, Greenberg determined the field of rationality of the p-torsion subgroup of Jp,s and moreover he proved that the λ3-torsion points of Jp,s are all rational over Q(ζ). In this paper we determine quite explicitly the λ3-torsion points of Jp,1 for p=5 and p=7, as well as some further p-torsion points which have interesting arithmetical applications, notably to the complementary laws of Kummer’s reciprocity for pth powers. 相似文献
7.
Tomas Antonius Klenke 《Journal of Number Theory》2005,110(2):387-395
Let E be an elliptic curve over an infinite field K with characteristic ≠2, and σ∈H1(GK,E)[2] a two-torsion element of its Weil-Châtelet group. We prove that σ is always visible in infinitely many abelian surfaces up to isomorphism, in the sense put forward by Cremona and Mazur in their article (J. Exp. Math. 9(1) (2000) 13). Our argument is a variant of Mazur's proof, given in (Asian J. Math. 3(1) (1999) 221), for the analogous statement about three-torsion elements of the Shafarevich-Tate group in the setting where K is a number field. In particular, instead of the universal elliptic curve with full level-three-structure, our proof makes use of the universal elliptic curve with full level-two-structure and an invariant differential. 相似文献
8.
9.
We show that if a finite group G is the Galois group of a Galois cover of over , then the orders p
n
of the abelianization of its p-Sylow subgroups are bounded in terms of their index m, of the branch point number r and the smallest prime of good reduction of the branch divisor. This is a new constraint for the regular inverse Galois problem: if p
n
is suitably large compared to r and m, the branch points must coalesce modulo small primes. We further conjecture that p
n
should be bounded only in terms of r and m. We use a connection with some rationality question on the torsion of abelian varieties. For example, our conjecture follows
from the so-called torsion conjectures. Our approach also provides a new viewpoint on Fried’s Modular Tower program and a
weak form of its main conjecture. 相似文献
10.
We study the potential density of rational points on double solids ramified along singular reduced sextic surfaces. Also, we investigate elliptic fibration structures on nonsingular sextic double solids defined over a perfect field of characteristic 5. 相似文献
11.
We present in this article several possibilities to approach the height of an algebraic curve defined over a number field: as an intersection number via the Arakelov theory, as a limit point of the heights of its algebraic points and, finally, using the minimal degree of Belyi functions. 相似文献
12.
R?zvan Li?canu 《Journal of Differential Equations》2004,207(1):93-116
We are describing Lamé differential operators with a full set of algebraic solutions. For each finite group G, we are describing the possible values of the degree parameter n such that the Lamé operator Ln has the projective monodromy group G. The main technical tool is the combinatorics associated to Belyi functions, ideas that we already used in (Rend. Sem. Mat. Univ. Padova 107 (2002) 191-208) for describing the case n=1. We also supply proofs to some finiteness properties conjectured by Baldassarri and by Dwork, and we work out an explicit formula for the number of essentially different Lamé equations when n=2. This approach can be generalized for arbitrary degree n (see (Counting Integral Lamé Equations by Means of Dessins d'Enfants, arXiv:math.CA/0311510) for n integer). 相似文献
13.
This paper proves a generalization of Shafarevich's Conjecture, for fields of Laurent series in two variables over an arbitrary field. This result says that the absolute Galois group GK of such a field K is quasi-free of rank equal to the cardinality of K, i.e. every non-trivial finite split embedding problem for GK has exactly proper solutions. We also strengthen a result of Pop and Haran-Jarden on the existence of proper regular solutions to split embedding problems for curves over large fields; our strengthening concerns integral models of curves, which are two-dimensional. 相似文献
14.
Sergio Albeverio 《Bulletin des Sciences Mathématiques》2006,130(8):697-706
An internal lifting for an arbitrary measurable Lévy process is constructed. This lifting reflects our intuitive notion of a process which is the infinitesimal sum of its infinitesimal increments, those in turn being independent from and closely related to each other - for short, the process can be regarded as some kind of random walk (where the step size generically will vary). The proof uses the existence of càdlàg modifications of Lévy processes and certain features of hyperfinite adapted probability spaces, commonly known as the “model theory of stochastic processes”. 相似文献
15.
16.
We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3n) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line
minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson
and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the
second uses the moduli interpretation.
Received: 30 September 2005 相似文献
17.
18.
We give a purely algebro-geometric proof of the fact that every nonsingular
projective curve can be defined over a finite extension of its moduli field.
This extends a result byWolfart [7] to curves over fields of arbitrary
characteristic.
Received: 30 November 2001 相似文献
19.
In this paper we consider the curves defined over and give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves . Our proof involves finding an exact formula for the number of -rational points on for all n, and uses a result we proved elsewhere about the number of rational points on supersingular curves. 相似文献
20.
Mark Kisin 《Mathematische Zeitschrift》2000,233(2):347-363
If is a a scheme of finite type over a local field F, and is a proper smooth family, then to each rational point one can assign an extension of the absolute Galois group of F by the geometric fundamental group G of the fibre . If F has uniformiser , and residue characteristic p, we show that the corresponding extension of the absolute Galois group of by the maximal prime to p quotient of G is locally constant in the -adic topology of . We give a similar result in the case of non-proper families, and families over -adic analytic spaces.
Received August 14, 1998 相似文献