Simplicial methods for operads and algebraic geometry

This book is an introduction to two new topics in homotopy theory: DendroidalSets (by Ieke Moerdijk) and Derived Algebraic Geometry (by Bertrand Toën). The category of dendroidal sets is an extension of that of simplicial sets, based on rooted trees instead of linear orders, suitable as a model category for higher topological structures. Derived algebraic geometry deals with functors from simplicial commutative rings to simplicial sets subject to a homotopical descent condition. The material in the book is an enhanced version of lecture notes from courses given within a special year on Homotopy Theory and Higher Categories at the CRM in Barcelona. The material is not available elsewhere, except in the original research articles The material is presented by the best experts, in fact the inventors themselves The exposition has maintained the directness of the original lectures INDICE: Part I: Lectures on Dendroidal Sets 1. Operads 2. Trees as operads3. Dendroidal sets 4. Tensor product of dendroidal sets 5. A Reedy model structure on dendroidal spaces 6. The Boardman-Vogt resolution and homotopy coherent nerve 7. Inner Kan complexes and normal dendroidal sets 8. Model structureson dendroidal sets Part II: Simplicial Presheaves and Derived Algebraic Geometry 1. Motivation and objectives 2. Simplicial presheaves as stacks 3. Algebraic stacks 4. Simplicial commutative algebras 5. Derived stacks and derived algebraic stacks 6. Examples of derived algebraic stacks.

• ISBN: 978-3-0348-0051-8
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 186
• Fecha Publicación: 28/02/2011
• Nº Volúmenes: 1
• Idioma: Inglés