Sheaves on finite posets and modules over normal semigroup rings
✍ Scribed by Kohji Yanagawa
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 225 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
Recently, the local cohomology module H i I (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
More precisely, we will study the local cohomology modules H i I (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 H i I (R) are always ÿnite in the simplicial case. If R is not simplicial, this is not true as a famous example of Hartshorne shows.