This article grew out of lectures given in the programme “Interactions between
Representation Theory, Algebraic Topology, and Commutative Algebra”(IRTATCA) at the …

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We give homotopy invariant definitions corresponding to three well-known properties of
complete intersections, for the ring, the module theory and the endomorphisms of the …

We study complexes of finite complete intersection dimension in the derived category of a
local ring. Given such a complex of complexity c, we prove that the thick subcategory it …

We establish an upper bound for the cochain type level of the total space of a pull-back
fibration. It explains to us why the numerical invariants for principal bundles over the sphere …

We investigate various homotopy invariant formulations of commutative algebra in the
context of rational homotopy theory. The main subject is the complete intersection condition …

Homotopy invariant notions of complete intersection in algebra and topology - Growth and
periodicity Page 1 Complete intersections Benson, Greenlees, Hess, Shamir Commutative …