Abstract
Let be a finite group and be a field of characteristic . We investigate the homotopy category of the category of complexes of injective ( projective) -modules. If is a -group, this category is equivalent to the derived category of the cochains on the classifying space; if is not a -group, it has better properties than this derived category. The ordinary tensor product in with diagonal -action corresponds to the tensor product on .
We show that can be regarded as a slight enlargement of the stable module category . It has better formal properties inasmuch as the ordinary cohomology ring is better behaved than the Tate cohomology ring .
It is also better than the derived category , because the compact objects in form a copy of the bounded derived category , whereas the compact objects in consist of just the perfect complexes.
Finally, we develop the theory of support varieties and homotopy colimits in .
Citation
David Benson. Henning Krause. "Complexes of injective kG-modules." Algebra Number Theory 2 (1) 1 - 30, 2008. https://doi.org/10.2140/ant.2008.2.1
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