Homotopy theory of comodules over a Hopf algebroid

By Mark Hovey. 2003

94 citations recorded by the source corpus.

Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of comodules over a well-behaved Hopf algebroid (A, Gamma). That is, we construct the derived category Stable(Gamma) of (A, Gamma) as the homotopy category of a Quillen model structure on the category of unbounded chain complexes of Gamma-comodules. This derived category is obtained by inverting the homotopy isomorphisms, NOT the homology isomorphisms. We establish the basic properties of Stable(Gamma), showing that it is a compactly generated tensor triangulated category.

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

View Paper: https://www.semanticscholar.org/paper/3edf300d18def1c89636674395123c189d70ff0b

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In Algebra and Number Theory

1. Bogdan Gheorghe
2. Zhouli Xu
3. Guozhen Wang

In Geometry and Topology

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3. Guozhen Wang

In Mathematical Physics

1. Bogdan Gheorghe
2. Zhouli Xu
3. Guozhen Wang

Citations in the corpus

• The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “(29) Stable(BP∗BP): the underlying stable ∞-category of Hovey’s unbounded derived category of BP∗BP-comodules.”