Derived Manifolds from Functors of Points

Download or read book Derived Manifolds from Functors of Points written by Franz Vogler and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.