ON SOME TWISTED COHOMOLOGY OF THE RING OF INTEGERS

• 발행기관: 충청수학회
• 저자명: Seok-Min Lee
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 30, No. 1, 77~102쪽, 전체 26쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2017.02.28

국문 초록

As an analogy of Poincar´e series in the space of modular forms, T. Ono associated a module M c /P c for γ = [c] ∈ H 1 (G, R × ) where finite group G is acting on a ring R. M c /P c is re-garded as the 0-dimensional twisted Tate cohomology b H 0 (G, R + ) γ . In the case that G is the Galois group of a Galois extension K of a number field k and R is the ring of integers of K, the vanishing properties of M c /P c are related to the ramification of K/k. We generalize this to arbitrary n-dimensional twisted cohomology of the ring of integers and obtain the extended version of theorems. More-over, some explicit examples on quadratic and biquadratic number fields are given.

목차

1. Introduction

2. n-dimensional twisted cohomology

3. Galois extension of number fields

4. 1-dimensional twisted cohomology

5. Local and global

6. Quadratic fields

7. Biquadratic fields

키워드

twisted cohomology twisted module Poincar´e sum biquadratic field.