Escudo de la República de Colombia
Sistema Nacional de Biliotecas - Repositorio Institucional Universidad Nacional de Colombia Biblioteca Digital - Repositorio Institucional UN Sistema Nacional de Bibliotecas UN

Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory

Vivares Parra, Carlos Eduardo (2015) Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.

Texto completo

[img]
Vista previa
PDF - Versión Aceptada
Available under License Creative Commons Attribution Non-commercial No Derivatives.

680kB

Resumen

The notion of stack grew out of attempts to parameterize geometric objects varying in families. Such families are classically know as Moduli and their understanding is a central theme in Algebraic Geometry. The formalism of stacks was introduced by A. Grothendieck and M. Artin as the natural context in which moduli problems of objects with symmetries can be tackled. The usual spaces used in geometry– Manifolds, Varieties, Schemes– are inadequate for the parametrization of geometry objects that are self similar. Instead one needs a procedure that will not only encode the way things vary in families but will also remembers the intrinsic symmetries of each object in the family. As an example, let us consider two families of ellipses parametrized by a circle: The left-hand family is trivial, all the ellipses in this one are positioned in exactly the same way. The ellipses in the right-hand family are all the same but they are rotated in their planes. Families of this kind are called isotrivial. The usual parameter spaces do not capture the distinction between trivial and isotrivial families.

Tipo de documento:Tesis/trabajos de grado - Thesis (Maestría)
Colaborador / Asesor:Vélez Caicedo, Juan Diego
Temática:5 Ciencias naturales y matemáticas / Science > 51 Matemáticas / Mathematics
Unidad administrativa:Sede Medellín > Facultad de Ciencias > Escuela de Matemáticas
Código ID:51249
Enviado por : bdigital1_ med
Enviado el día :16 Mar 2016 16:24
Ultima modificación:17 May 2018 16:45
Ultima modificación:17 May 2018 16:45
Exportar:Clic aquí
Estadísticas:Clic aquí
Compartir:

Solamente administradores del repositorio: página de control del ítem

Vicerrectoría de Investigación: Número uno en investigación
Indexado por:
Indexado por Scholar Google WorldCat DRIVER Metabiblioteca OAIster BASE BDCOL Registry of Open Access Repositories SNAAC Red de repositorios latinoamericanos eprints Open archives La referencia Tesis latinoamericanas OpenDOAR CLACSO
Este sitio web se ve mejor en Firefox