Boundedness of cohomology

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• 作者：Markus Brodmann ; Maryam Jahangiri ; Cao Huy Linh
• 关键词：Local cohomology ; Sheaf cohomology ; Graded modules ; Projective schemes ; Finiteness of cohomology
• 刊名：Journal of Algebra
• 出版年：2010
• 出版时间：15 January 2010
• 年：2010
• 卷：323
• 期：2
• 页码：458-472
• 全文大小：238 K

文摘

Let and let denote the class of all pairs (R,M) in which is a Noetherian homogeneous ring with Artinian base ring R₀ and such that M is a finitely generated graded R-module of dimension d. For such a pair (R,M) let denote the (finite) R₀-length of the n-th graded component of the i-th R₊-transform module .

The cohomology table of a pair is defined as the family of non-negative integers . We say that a subclass of is of finite cohomology if the set is finite. A set is said to bound cohomology, if for each family of non-negative integers, the class is of finite cohomology. Our main result says that this is the case if and only if contains a quasi diagonal, that is a set of the form {(i,n_i)i=0,…,d−1} with integers n₀>n₁>>n_d−1.

We draw a number of conclusions of this boundedness criterion.