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Derived Manifolds from Functors of Points

Augsburger Schriften zur Mathematik, Physik und Informatik , Bd. 22

Franz Vogler

ISBN 978-3-8325-3405-9
158 pages, year of publication: 2013
price: 35.00 €
In this thesis a functorial approach to the category of derived manifolds is developed. We use a similar approach as Demazure and Gabriel did when they described the category of schemes as a full subcategory of the category of sheaves on the big Zariski site. Their work is further developed leading to the definition of C#-schemes and derived manifolds as certain sheaves on appropriate big sites. The new description of C#-schemes and derived manifolds via functors is compared to the previous approaches via locally ringed spaces given by D. Joyce and D. Spivak. Furthermore, it is proven that both approaches lead to equivalent categories.

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Keywords:
  • derived manifolds
  • C#-schemes
  • model categories
  • functor of points

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