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SOME RESULTS IN QUOTIENT STACKS | |

DIEGO ALEXANDER ACOSTA ALVAREZ | |

Acceso Abierto | |

Atribución-NoComercial | |

FIBRED CATEGORIES | |

Many interesting kind of geometric-algebraic stacks are defined as the quotient stack associated to a groupoid in algebraic spaces. More precisely, if (U; R; s; t; c) is a groupoid in algebraic spaces we have the quotient stack [U=R]. Some of them are quotients by the action of a group space into an algebraic space. When we have 1-morphisms X 􀀀! Z and Y 􀀀! Z of quotient stacks, some natural questions arise: if a fibre or a 2-fibre product exists, is this also a quotient stack? If the answer is armative, what is the associated groupoid? What if one of those 1-morphisms has an special property like to be an open immersion? In this work we are going to give some results about these questions, trying to solve it in the most general possible case. While in categories over a fixed category C there are always a fibre product and a 2-fibre product, when we are working with fibred categories we have found that a fibre product does not always exist. However, we found a condition about the fibred product as a category over C and a class of fibred categories and 1-morphisms for which fibre product can always be constructed. We say that the fibre product has componentwise pullbacks if it satisfies that condition. In particular, when we define a quotient stack as the stackification of the fibred category associated to a functor induced by a groupoid in algebraic spaces, the fibred category belongs to this class and we can take the fibre product | |

27-08-2016 | |

Trabajo de grado, doctorado | |

OTRAS | |

Versión aceptada | |

acceptedVersion - Versión aceptada | |

Appears in Collections: | Tesis del CIMAT |

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