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Simplicial Methods for Operads and Algebraic Geometry

Name: Simplicial Methods for Operads and Algebraic Geometry
Brand: Birkhauser Verlag AG
SKU: 9783034800518
Price: 24.56 EUR
Availability: InStock

Autor: Ieke Moerdijk, Bertrand Toën

Jazyk:

Väzba: Brožovaná

Vydavateľ: Birkhauser Verlag AG

Dostupnosť: Skladom u dodávateľa

Odosielame za 8-11 dní

24.56 €

This book is an introduction to two new topics in homotopy theory: Dendroidal Sets (by Ieke Moerdijk...

Informácie o knihe

Autor

Ieke Moerdijk, Bertrand Toën

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2010

Stránok

186

EAN

9783034800518

ISBN

3034800517

Enbook ID

01438828

Vydavateľ

Birkhauser Verlag AG

Hmotnosť

336

Rozmery

169 x 239 x 11

Kompletný popis

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.This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods.§Moerdijk s lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena. For example, dendroidal sets admit a closed symmetric monoidal structure related to the Boardman Vogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with a suitable model structure on the category of dendroidal sets. Important concepts are illustrated with pictures and examples.§The lecture series by Toën presents derived algebraic geometry. While classical algebraic geometry studies functors from the category of commutative rings to the category of sets, derived algebraic geometry is concerned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derived quotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent condition. These lectures provide a concise and focused introduction to this vast subject, glossing over many of the technicalities that make the subject s research literature so overwhelming.§Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Toën s lectures, some background in algebraic geometry is also necessary.