Infinite class towers for function fields

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود 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

Infinite Hilbert Class Field Towers over Cyclotomic Fields

Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...

متن کامل

Everywhere Ramified Towers of Global Function Fields

We construct a tower of function fields F0 ⊂ F1 ⊂ . . . over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] <∞. We also construct a tower in which every place ramifies and limNFi/[Fi : F0] > 0, where NFi is the number of degree-1 places of Fi. These towers answer questions posed by Stichtenoth at Fq7.

متن کامل

Towers of function fields with extremal properties

For F/K an algebraic function field in one variable over a finite field of constants K (i.e., F is a finite algebraic extension of K(x) where x ∈ F is transcendental over K), let N(F ) and g(F ) denote the number of places of degree one and the genus, respectively, of F . Let F = (F1, F2, F3, . . .) be a tower of function fields, each defined over K. Further, we will assume that F1 ⊆ F2 ⊆ F3 . ...

متن کامل

Towers of Function Fields over Non-prime Finite Fields

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(`), for ` = p with p prime and n > 3 odd. A modular interpretation of the towers is given as well.

متن کامل

On 2-class field towers of imaginary quadratic number fields

For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.

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 of Number Theory

سال: 2013

ISSN: 0022-314X

DOI: 10.1016/j.jnt.2012.04.001