Operads, algebras, modules and motives

By Igor Kríz, A. J. May. Astérisque, 2018

173 citations recorded by the source corpus.

With motivation from algebraic topology, algebraic geometry, and string theory, we study various topics in differential homological algebra. The work is divided into five largely independent parts: I Definitions and examples of operads and their actions II Partial algebraic structures and conversion theorems III Derived categories from a topological point of view IV Rational derived categories and mixed Tate motives V Derived categories of modules over E∞ algebras In differential algebra, operads are systems of parameter chain complexes for multiplication on various types of differential graded algebras “up to homotopy”, for example commutative algebras, n-Lie algebras, n-braid algebras, etc. Our primary focus is the development of the concomitant theory of modules up to homotopy and the study of both classical derived categories of modules over DGA’s and derived categories of modules up to homotopy over DGA’s up to homotopy. Examples of such derived categories provide the appropriate setting for one approach to mixed Tate motives in algebraic geometry, both rational and integral.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6296111fe21c079a31c7a4b36d44fb5e630ee266

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

From Hag To Dag: Derived Moduli Stacks (2002, background): “studied in [Ha, De]. 3. The model category C(k) of complexes over some ring k and the tensor product of complexes (see [Ho, §2.3]). Commutative monoid-like objects are commutative E∞-algebras over k ([Kr-Ma]). The corresponding geometry is the so-called derived algebraic geometry that we are going t”