Ideal Class Groups, Some Computations

نویسندگان

چکیده

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

On the rank of ideal class groups

We review some questions of Shafarevich on the structure of ideal class groups of number elds, and discuss results that provide evidence in support of these questions. The analogy between number elds and algebraic function elds of one variable has long been a fruitful source of inspiration for the development of algebraic number theory. Hilbert's pioneering work in class eld theory, for instanc...

متن کامل

Cubic Structures and Ideal Class Groups

We establish a generalization of Breen’s theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec (Z) by relating this set to certain corresponding eigenspaces of...

متن کامل

Ideal Class Groups of Cyclotomic Number Fields I

Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse’s unit...

متن کامل

Galois Modules, Ideal Class Groups and Cubic Structures

We establish a connection between the theory of cyclotomic ideal class groups and the theory of “geometric” Galois modules and obtain results on the Galois module structure of coherent cohomology groups of Galois covers of varieties over Z. In particular, we show that an invariant that measures the obstruction to the existence of a virtual normal integral basis for the coherent cohomology of su...

متن کامل

Cyclic Subgroups of Ideal Class Groups in Real Quadratic Orders

The primary purpose of this paper is to provide general sucient conditions for any real quadratic order to have a cyclic subgroup of order n 2 N in its ideal class group. This generalizes results in the literature, including some seminal classical works. This is done with a simpler approach via the interplay between the maximal order and the non-maximal orders, using the underlying infrastruct...

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: 1995

ISSN: 0022-314X

DOI: 10.1006/jnth.1995.1019