## Local Picard group of pointed monoids and their algebras

Autor(en): | Alberelli, Davide Brenner, Holger |

Stichwörter: | Mathematics; Picard group; simplicial complex; Stanley-Reisner rings; VECTOR-BUNDLES |

Erscheinungsdatum: | 2019 |

Herausgeber: | TAYLOR & FRANCIS INC |

Journal: | COMMUNICATIONS IN ALGEBRA |

Volumen: | 47 |

Ausgabe: | 6, SI |

Startseite: | 2308 |

Seitenende: | 2340 |

Zusammenfassung: | The main goal of this article is to give an explicit formula for H-Zar(j) (Spec center dot K[Delta], O-K[Lambda](+) in terms of simplicial and reduced simplicial cohomology, where K[Delta] is the Stanley- Reisner ring of the simplicial complex Delta. In particular, we compute the local Picard group of K[Delta]. To achieve this, we study the corresponding purely combinatorial problem on the punctured spectrum of the pointed monoid defined by Delta. The cohomology of the sheaf of units on Spec.K[Delta] is then the direct sum of this combinatorial cohomology, which has a decomposition along the vertices, and another part depending on the field K. |

ISSN: | 00927872 |

DOI: | 10.1080/00927872.2018.1492592 |

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