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Simplicial commutative algebras

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)


In this lecture we review the homotopy theory of simplicial commutative rings. It will be used throughout the next lectures in order to define and study the notion of derived schemes and derived stacks.


  • Commutative Ring
  • Homotopy Category
  • Natural Morphism
  • Homotopy Pullback
  • Model Category Structure

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Correspondence to Ieke Moerdijk .

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Moerdijk, I., Toën, B. (2010). Simplicial commutative algebras. In: Simplicial Methods for Operads and Algebraic Geometry. Advanced Courses in Mathematics - CRM Barcelona. Springer, Basel.

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