E-Book, Englisch, 186 Seiten, eBook
Moerdijk / Toën Simplicial Methods for Operads and Algebraic Geometry
2010
ISBN: 978-3-0348-0052-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 186 Seiten, eBook
Reihe: Advanced Courses in Mathematics - CRM Barcelona
ISBN: 978-3-0348-0052-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book is an introduction to two new topics in homotopy theory: Dendroidal Sets (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.
Zielgruppe
Graduate
Autoren/Hrsg.
Weitere Infos & Material
Lectures on Dendroidal Sets.- Operads.- Trees as operads.- Dendroidal sets.- Tensor product of dendroidal sets.- A Reedy model structure on dendroidal spaces.- Boardman–Vogt resolution and homotopy coherent nerve.- Inner Kan complexes and normal dendroidal sets.- Model structures on dendroidal sets.- Simplicial Presheaves and Derived Algebraic Geometry.- Motivation and objectives.- Simplicial presheaves as stacks.- Algebraic stacks.- Simplicial commutative algebras.- Derived stacks and derived algebraic stacks.- Examples of derived algebraic stacks.
