Degree bounds for projective division fields associated to elliptic modules with a trivial endomorphism ring

نویسندگان

چکیده

Let $k$ be a global field, let $A$ Dedekind domain with $\text{Quot}(A) = k$, and $K$ finitely generated field. Using unified approach for both elliptic curves Drinfeld modules $M$ defined over having trivial endomorphism ring, $k= \mathbb{Q}$, $A \mathbb{Z}$ in the former case function its ring of functions regular away from fixed prime latter case, any nonzero ideal $\mathfrak{a} \lhd A$ we prove best possible estimates norm $|\mathfrak{a}|$ degrees subfields $\mathfrak{a}$-division fields by scalars.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

9.1 Elliptic Curves with a given Endomorphism Ring

and we know that this ring is isomorphic to Z or an order O in an imaginary quadratic field K; in fact, the ring on the right is equal to Z or O (viewed as a subring of C).1 To simplify the discussion, we shall treat the isomorphism in (1) as an equality and view elements of End(EL) as elements of Z or O. How might we construct an elliptic curve with endomorphism ring O? An obvious way is to us...

متن کامل

ON PROJECTIVE L- MODULES

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

متن کامل

Modules with Dedekind Finite Endomorphism Rings

This article is a survey of modules whose endomorphism rings are Dedekind finite, Hopfian or co-Hopfian. We summarise the properties of such modules and present unified proofs of known results and generalisations to new structure theorems. MSC 2010. 16S50, 16D80.

متن کامل

A Note on a graph associated to a commutative ring

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...

متن کامل

Torsion bounds for elliptic curves and Drinfeld modules

We derive asymptotically optimal 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 attached to elliptic curves and Drinfeld modules, due to Serre and Pink-Rütsche, respectively. Our approach...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal de Theorie des Nombres de Bordeaux

سال: 2021

ISSN: ['1246-7405', '2118-8572']

DOI: https://doi.org/10.5802/jtnb.1153