Homological algebra and group representations

A standard invariant of a module over a ring is its annihilator, the collection of elements in the ring that multiply as zero on the module. Some geometry can be added by considering the collection of all prime ideals or maximal ideals of the ring that contain the annihilator. Using group cohomology, similar structures can be made to give rough classifications of modular representations of finite groups. Going further, it leads to a classifiction of some distinctve structures in the category of modules over the finite group. We will present an overview of this subject

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