### Abstract

Let S be a toric algebra over a field K of characteristic 0 and let I be a monomial ideal of S. We show that the local cohomology modules H _{i} ^{I} (S) are of finite length over the ring of differential operators D(S;K), generalizing the classical case of a polynomial algebra S. As an application, we compute the characteristic cycles of some local cohomology modules.

Original language | English |
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Pages (from-to) | 2461-2478 |

Number of pages | 18 |

Journal | Transactions of the American Mathematical Society |

Volume | 364 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 Feb 10 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Transactions of the American Mathematical Society*, vol. 364, no. 5, pp. 2461-2478. https://doi.org/10.1090/S0002-9947-2012-05372-4

**D-module structure of local cohomology modules of toric algebras.** / Hsiao, Jen-Chieh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - D-module structure of local cohomology modules of toric algebras

AU - Hsiao, Jen-Chieh

PY - 2012/2/10

Y1 - 2012/2/10

N2 - Let S be a toric algebra over a field K of characteristic 0 and let I be a monomial ideal of S. We show that the local cohomology modules H i I (S) are of finite length over the ring of differential operators D(S;K), generalizing the classical case of a polynomial algebra S. As an application, we compute the characteristic cycles of some local cohomology modules.

AB - Let S be a toric algebra over a field K of characteristic 0 and let I be a monomial ideal of S. We show that the local cohomology modules H i I (S) are of finite length over the ring of differential operators D(S;K), generalizing the classical case of a polynomial algebra S. As an application, we compute the characteristic cycles of some local cohomology modules.

UR - http://www.scopus.com/inward/record.url?scp=84856650168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856650168&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2012-05372-4

DO - 10.1090/S0002-9947-2012-05372-4

M3 - Article

VL - 364

SP - 2461

EP - 2478

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -