Establishes that the singularity category of C^*(BG; k) is the bounded derived category of the Ω-Tate spectrum, together with Gorenstein and Tate dualities and a Koszul construction under complete intersection assumptions.
Homotopy Invariant Commutative Algebra over fields
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abstract
These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in representation theory of groups, in classical algebraic topology and elsewhere. The notes grew out of a series of lectures given during the `Interactions between Representation Theory, Algebraic Topology and Commutative Algebra' (IRTATCA) at the CRM (Barcelona) in Spring 2015.
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The singularity category and duality for complete intersection groups
Establishes that the singularity category of C^*(BG; k) is the bounded derived category of the Ω-Tate spectrum, together with Gorenstein and Tate dualities and a Koszul construction under complete intersection assumptions.