Group Cohomology of the Universal Ordinary Distribution

نویسنده

  • YI OUYANG
چکیده

Abstract. For any odd squarefree integer r, we get complete description of the Gr = Gal(Q(μr)/Q) group cohomology of the universal ordinary distribution Ur in this paper. Moreover, if M is a fixed integer which divides l−1 for all prime factors l of r, we study the cohomology group H(Gr, Ur/MUr). In particular, we explain the mysterious construction of the elements κr′ for r |r in Rubin[10], which come exactly from a certain Z/MZ-basis of the cohomology group H(Gr, Ur/MUr) through an evaluation map.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Universal Norm Distribution

We introduce and study the universal norm distribution in this paper, which generalizes the concepts of universal ordinary distribution and the universal Euler system. We study the Anderson type resolution of the universal norm distribution and then use this resolution to study the group cohomology of the universal norm distribution.

متن کامل

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

متن کامل

A double complex for computing the sign-cohomology of the universal ordinary distribution

3 The principal objects of study 17 3.1 The basic data (K, A, sgn ) . . . . . . . . . . . . . . . . . . . . 17 3.2 A-lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 The set Ξ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.4 The profinite group G . . . . . . . . . . . . . . . . . . . . . . 20 3.5 The sign group G∞ . . . . . . . . . . . . . . . . . . . . ...

متن کامل

A Note on Cyclotomic Euler Systems and the Double Complex Method

Let F be a finite real abelian extension of Q. Let M be an odd positive integer. For every squarefree positive integer r the prime factors of which are congruent to 1 modulo M and split completely in F, the corresponding Kolyvagin class κr ∈ F×/F×M satisfies a remarkable and crucial recursion which for each prime number l dividing r determines the order of vanishing of κr at each place of F abo...

متن کامل

Ordinary I?o(g)-graded Cohomology

Let G be a compact Lie group. What is the appropriate generalization of singular cohomology to the category of G-spaces XI The simplest choice is the ordinary cohomology of EG xG X, where EG is the total space of a universal principal G-bundle. This Borel cohomology [1] is readily computable and has many applications, but is clearly inadequate for such basic parts of G-homotopy theory as obstru...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008