Sheaves on finite posets and modules over normal semigroup rings
Sheaves on finite posets and modules over normal semigroup rings
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普通半群环上有限偏序集和模上的滑轮
DOI：
10.1016/s0022-4049(00)00095-5
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发表时间：
2001
影响因子：
0.8
通讯作者：
Kohji Yanagawa
中科院分区：
文献类型：
--
作者：
Kohji Yanagawa
最近，几位作者研究了具有单项理想I中支集的多项式环S的局部上同调模HII(S)。本文将这些结果推广到C∈ZD的正规Gorenstein半群环R=k[XC|c⊂C]上。更确切地说，我们将研究单项理想I中有支集的局部上同调模HII(R)及其内射分解。粗略地说，我们将看到它们只依赖于与R相关的多面体的面格的组合性质。因此，如果R是单形的，那么在我们的上下文中它的行为就像多项式环一样。例如，在单纯情形下，HII(R)的Bass数总是有限的。如果R不是单形的，这不是真的，正如哈特肖恩的一个著名例子所表明的那样。
Recently, the local cohomology module HIi(S) of a polynomial ring S with supports in a monomial ideal I has been studied by several authors. In the present paper, we will extend these results to a normal Gorenstein semigroup ring R=k[xc|c∈C] of C⊂ Zd. More precisely, we will study the local cohomology modules HIi(R) with supports in monomial ideals I, and their injective resolutions. Roughly speaking, we will see that they only depend on the combinatorial properties of the face lattice of a polytope associated to R. Hence, if R is simplicial, it behaves just like a polynomial ring in our context. For example, the Bass numbers of HIi(R) are always finite in the simplicial case. If R is not simplicial, this is not true as a famous example of Hartshorne shows.
影响因子：
0.9
作者：
Kohji Yanagawa
通讯作者：
Kohji Yanagawa