التفاصيل البيبلوغرافية
| العنوان: |
Cohomological dimension of DG-modules. |
| المؤلفون: |
Rao, Yanping, Liu, Zhongkui, Yang, Xiaoyan |
| المصدر: |
Journal of Algebra & Its Applications; Mar2024, Vol. 23 Issue 4, p1-14, 14p |
| مصطلحات موضوعية: |
VANISHING theorems, NOETHERIAN rings |
| مستخلص: |
Let A be a commutative noetherian non-positive DG-ring, ̄ an ideal of Ā : = H 0 (A) , and M ∈ D (A). In this paper, we introduce the notion of cohomological dimension of DG-modules and investigate the interplay between cd A ( ̄ , M) : = sup { cd Ā ( ̄ , H n (M)) + n | n ∈ ℤ } and sup R Γ ̄ (M). It is shown that cd A ( ̄ , M) = sup R Γ ̄ (M) for any 0 ≇ M ∈ D f − (A). As an application, we recover a DG-version of Grothendieck's vanishing and non-vanishing theorems for local cohomology. We also study the cohomological dimension of Koszul DG-modules and get some interesting results. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
