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Model categories and tilting modules for algebraic groups

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If you have a question about this talk, please contact Zhen Lin Low.

Let A be a ring. Then A-mod is an abelian category. If A is graded, then the category A-grmod (with homogeneous, degree 0 homomorphisms) is still abelian. What about if A is filtered? Then the category A-filtmod is not abelian in general, so the standard constructions from homological algebra don’t work. Yet not all is lost, if we are only interested in derived properties of filtered modules. I’ll show a quick and dirty way to get the derived category using model categories. Then I’ll show an application to the study of tilting modules for algebraic groups.

This talk is part of the Extraordinary Category Theory Seminar series.

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