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Deequivariantisation of indecomposable sheaves

The equivariant derived category here is the derived category of $\mathbb{Z}/2\mathbb{Z}$-modules. Now take the regular representation. It’s indecomposable. … If you forget the equivariant structure it decomposes. …
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3 votes

Deequivariantisation of indecomposable sheaves

Write $\underline{k}$ for the (equivariant) constant sheaf on $\mathbb{G}_m$ (i.e., monoidal unit). … The point, from the Koszul dual/algebraic perspective, is that any situation with torsion (i.e., where you can't obtain ordinary cohomology from equivariant cohomology) will lead to this. …
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