共查询到20条相似文献,搜索用时 15 毫秒
1.
Florian Breuer 《Journal of Number Theory》2010,130(5):1241-1250
We derive upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L:K]. Our main tool is the adelic openness of the image of Galois representations, due to Serre, Pink and Rütsche. Our approach is to prove a general result for certain Galois modules, which applies simultaneously to elliptic curves and to Drinfeld modules. 相似文献
2.
In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
3.
Satoshi Kondo 《Journal of Number Theory》2004,104(2):373-377
We define Eisenstein series and theta functions for Drinfeld modules of arbitrary rank, and prove an analog of Kronecker limit formula. 相似文献
4.
We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves. 相似文献
5.
Dragos Ghioca 《Journal of Number Theory》2007,125(1):85-94
We study the v-adic distance from the torsion of a Drinfeld module to an affine variety. 相似文献
6.
Dragos Ghioca 《Mathematische Annalen》2006,336(4):841-865
We prove an equidistribution result for torsion points of Drinfeld modules of generic characteristic. We also show that similar equidistribution statements would provide proofs for the Manin–Mumford and the Bogomolov conjectures for Drinfeld modules. 相似文献
7.
Let φ be a Drinfeld A-module of arbitrary rank and generic characteristic over a finitely generated field K. If the endomorphism ring of φ over an algebraic closure of K is equal to A, we prove that the image of the adelic Galois representation associated to φ is open. 相似文献
8.
Dragos Ghioca 《Journal of Number Theory》2007,123(2):426-455
We give a lower bound for the local height of a nontorsion element of a Drinfeld module. 相似文献
9.
Mihran Papikian 《Archiv der Mathematik》2009,92(4):291-302
We prove that there are only finitely many modular curves of -elliptic sheaves over which are hyperelliptic. In odd characteristic we give a complete classification of such curves.
The author was supported in part by NSF grant DMS-0801208 and Humboldt Research Fellowship. 相似文献
10.
Gert-Jan van der Heiden 《Monatshefte für Mathematik》2004,143(2):115-143
As is well-known, there exists a Weil pairing for elliptic curves which is a perfect bilinear form from the m-torsion of the elliptic curve E to the m-th roots of unity. In this paper we will show how Andersons paper [1] gives rise to an analogue of this pairing for Drinfeld modules.The author was supported by NWO Grant 613.007.040. The author would like to thank G. Böckle and S. J. Edixhoven for their comments. 相似文献
11.
Yifan Yang 《Advances in Mathematics》2006,204(2):481-508
We obtain defining equations of modular curves X0(N), X1(N), and X(N) by explicitly constructing modular functions using generalized Dedekind eta functions. As applications, we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup. We also use our model of X0(37) to find explicit modular parameterization of rational elliptic curves of conductor 37. 相似文献
12.
Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p. 相似文献
13.
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
14.
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
15.
Let K be a finitely generated field of transcendence degree 1 over a finite field, and set GK?Gal(Ksep/K). Let φ be a Drinfeld A-module over K in special characteristic. Set E?EndK(φ) and let Z be its center. We show that for almost all primes p of A, the image of the group ring Ap[GK] in EndA(Tp(φ)) is the commutant of E. Thus, for almost all p it is a full matrix ring over Z⊗AAp. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p] is absolutely irreducible for almost all p. 相似文献
16.
Mihran Papikian 《Archiv der Mathematik》2009,92(3):237-250
We prove a genus formula for modular curves of -elliptic sheaves. We use this formula to show that the reductions of modular curves of -elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of tends to infinity.
Received: 14 October 2008
The author was supported in part by NSF grant DMS-0801208 and Humboldt Research Fellowship. 相似文献
17.
In this work, we determine all modular curves X1(M,N) which are bielliptic, and then we also discuss the problem of finding the curves X1(M,N) which admit infinitely many quartic points over . 相似文献
18.
Matija Kazalicki 《Journal of Number Theory》2008,128(6):1662-1669
For every positive integer m, there is a unique Drinfeld modular function, holomorphic on the Drinfeld upper-half plane, jm(z) with the following t-expansion
19.
20.
A. Álvarez 《Journal of Number Theory》2005,110(2):279-316
In a paper from 1994, G.W. Anderson studies the relation between theta functions and rank-one Drinfeld modules. Here, we study generalized theta functions in relation to rank-n Drinfeld modules, explicitly obtaining Plucker coordinates for Drinfeld modules. 相似文献