Computing generators of the tame kernel of a global function field
نویسنده
چکیده
The group K2 of a curve C over a finite field is equal to the tame kernel of the corresponding function field. We describe two algorithms for computing generators of the tame kernel of a global function field. The first algorithm uses the transfer map and the fact that the `-torsion can easily be described if the ground field contains the `th roots of unity. The second method is inspired by an algorithm of Belabas and Gangl for computing generators of K2 of the ring of integers in a number field. We finally give the generators of the tame kernel for some elliptic function fields. c © 2006 Elsevier Ltd. All rights reserved.
منابع مشابه
Bounds for computing the tame kernel
The tame kernel of the K2 of a number field F is the kernel of some explicit map K2F → ⊕ k∗ v , where the product runs over all finite primes v of F and kv is the residue class field at v. When S is a set of primes of F , containing the infinite ones, we can consider the S-unit group US of F . Then US ⊗ US has a natural image in K2F . The tame kernel is contained in this image if S contains all...
متن کاملUsing and comparing metaheuristic algorithms for optimizing bidding strategy viewpoint of profit maximization of generators
With the formation of the competitive electricity markets in the world, optimization of bidding strategies has become one of the main discussions in studies related to market designing. Market design is challenged by multiple objectives that need to be satisfied. The solution of those multi-objective problems is searched often over the combined strategy space, and thus requires the simultaneous...
متن کاملTame Kernels and Further 4-rank Densities
Abstract. There has been recent progress on computing the 4-rank of the tame kernel K2(OF ) for F a quadratic number field. For certain quadratic number fields, this progress has led to “density results” concerning the 4-rank of tame kernels. These results were first mentioned in [6] and proven in [8]. In this paper, we consider some additional quadratic number fields and obtain further density...
متن کاملGenerators and Relations for K
Tate’s algorithm for computing K2OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order—the latter, together with some structural results on the p-primary part of K2OF due to Tate and Keune, gives a proof of its structure for many number fields of small discriminants, confirming earlier conjectural...
متن کاملThe 3-adic regulators and wild kernels
For any number field, J.-F. Jaulent introduced a new invariant called the group of logarithmic classes in 1994. This invariant is proved to be closely related to the wild kernels of number fields. In this paper, we show how to compute the kernel of the natural homomorphism from the group of logarithmic classes to the group of p-ideal classes by computing the p-adic regulator which is a classica...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 41 شماره
صفحات -
تاریخ انتشار 2006