Model theory of profinite groups having the Iwasawa property

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

Profinite Groups

γ = c0 + c1p+ c2p + · · · = (. . . c3c2c1c0)p, with ci ∈ Z, 0 ≤ ci ≤ p− 1, called the digits of γ. This ring has a topology given by a restriction of the product topology—we will see this below. The ring Zp can be viewed as Z/pZ for an ‘infinitely high’ power n. This is a useful idea, for example, in the study of Diophantine equations: if such an equation has a solution in the integers, then it...

متن کامل

Cohomology of Profinite Groups

A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible...

متن کامل

Cohomology of Profinite Groups

The aim of this thesis is to study profinite groups of type FPn. These are groups G which admit a projective resolution P of Ẑ as a ẐJGK-module such that P0, . . . , Pn are finitely generated, so this property can be studied using the tools of profinite group cohomology. In studying profinite groups it is often useful to consider their cohomology groups with profinite coefficients, but pre-exis...

متن کامل

Root numbers, Selmer groups, and non-commutative Iwasawa theory

Global root numbers have played an important role in the study of rational points on abelian varieties since the discovery of the conjecture of Birch and Swinnerton-Dyer. The aim of this paper is to throw some new light on this intriguing and still largely conjectural relationship. The simplest avatar of this phenomenon is the parity conjecture which asserts that for an abelian variety A over a...

متن کامل

Computations About Tate-Shafarevich Groups Using Iwasawa Theory

We explain how to combine deep results from Iwasawa theory with explicit computation to obtain information about p-parts of Tate-Shafarevich groups of elliptic curves over Q. This method provides a practical way to compute #X(E/Q)(p) in many cases when traditional p-descent methods are completely impractical and also in situations where results of Kolyvagin and Kato do not apply.

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: Illinois Journal of Mathematics

سال: 1998

ISSN: 0019-2082

DOI: 10.1215/ijm/1255985614