Problems on coeficient ideals

Thời gian: 14:00 đến 15:30 Ngày 14/05/2019

Địa điểm: C2-714, VIASM

Báo cáo viên: Prof. Ngo Viet Trung (Institute of Mathematics, Hanoi)

Tóm tắt:

Let I be an ideal in a local ring (A,m).

For any ideal J \supset I with l(J/I) < \infty, Amao showed that the function l(J^n/I^n) is a polynomial for n >> 0.

Let P(J/I,n) denote this polynomial.

If A is quasi-unmixed, Herzog, Puthenpurakal and Verma showed that for k = 0,...,s, where s is the analytic of I, there exists a largest ideal I_k with l(I_k/I) < \infty and dim P(J/I,n) \le s - k.

These ideals are called the coefficient ideals of I.

If I is an m-primary ideal, then I_0 is the integral closure and I_s the Ratliff-Rush closure of I.

In this talk I will give a brief summary on what are known on coefficient ideals and raise some problems.